Page 4 : 12/03/2022, 18:04, , Plus Two Maths Chapter Wise Questions and Answers Chapter 10 Vector Algebra – HSSLive Guru, −, −, , (ii) If the projection of ā on another vector ¯, b is √14 , which among the following, could be ¯, b ? (1), (a) i + j + k, (b) 6i + 2j + 4k, (c) 3i – j + 2k, (d) 2i + 3j + k, (iii) If ā makes an angle 60° with a vector c̄ , find the projection of ā on c̄ (1), Answer:, , −, −, , ¯, (ii) Since projection of ā on another vector ¯, b and magnitude of ā is √14 , then ā and b, , are parallel, (b) 6i + 2j + 4k., (iii) Projection of ā on c̄, −, −, , = |ā|cos60° = √14 ×, , 1, 2, , =, , √14, 2, , ., , Question 8., (i) The projection of the vector 2i + 3j + 2k on the vector i + j + k is (1), , (ii) Find the area of a parallelogram whose adjacent sides are the vectors 2i + j + k and, 6i – j (2), Answer:, Plus Two Maths Vector Algebra 3 Mark Questions and Answers 10, (ii) Let ā = 2i + j + k, ¯, b =i–j, , = i(0 + 1) – j(0 – 1) + k(-2 – 1 ) = i + j -3k, Area =, , Question 9., (i) The angle between the vectors i + j and j + k is (1), https://hssliveguru.com/plus-two-maths-chapter-wise-questions-and-answers-chapter-10/, , 4/19

Page 5 : 12/03/2022, 18:04, , Plus Two Maths Chapter Wise Questions and Answers Chapter 10 Vector Algebra – HSSLive Guru, , (a) 60°, (b) 30°, (c) 45°, (d) 90°, , Answer:, (i) (a) 60°, , Question 10., , Answer:, , https://hssliveguru.com/plus-two-maths-chapter-wise-questions-and-answers-chapter-10/, , 5/19

Page 6 : 12/03/2022, 18:04, , Plus Two Maths Chapter Wise Questions and Answers Chapter 10 Vector Algebra – HSSLive Guru, , (ii) Given, ā + ¯, b + ā = 0̄, squaring both sides we get, , Plus Two Maths Vector Algebra Four Mark Questions and, Answers, Question 1., Let A (2, 3), B (1, 4), C (0, -2) and D (x, y) are vertices of a parallelogram ABCD., 1. Write the position vectors A, B, C and D. (2), 2. Find the value of x and y. (2), Answer:, 1. Position vector of A = 2i + 3 j, Position vector of B = i + 4j, Position vector of C = 0i – 2j, Position vector of D = xi + yj., 2. Since ABCD is a parallelogram, then, , (1) ⇒ -i + j = -xi – (y + 2 )j, x = 1, -2 – y = 1 ⇒ y = -3, ∴ D is (1, -3)., , https://hssliveguru.com/plus-two-maths-chapter-wise-questions-and-answers-chapter-10/, , 6/19

Page 7 : 12/03/2022, 18:04, , Plus Two Maths Chapter Wise Questions and Answers Chapter 10 Vector Algebra – HSSLive Guru, , Question 2., Find the position vector of a point R which divides the line joining the two points P, and Q whose vectors i + 2j – k and -i + j + k in the ratio 2:1, 1. internally and, 2. externally., Answer:, ¯, ¯¯¯¯¯, ¯, ¯, , OP, , ¯, ¯¯¯¯¯¯, ¯, , = i + 2j – k, OQ = -i + j + k, , Let R be the position vector of the dividing point,, 1., , 2., , Question 3., (i) Choose the correct answer from the bracket. If a unit vector â makes angles, with i and, (a), , π, , (b), , π, , (c), , π, , (d), , π, , 6, , 4, , 3, , 2, , π, 3, , π, 4, , with j and acute angle θ with k. then θ is, , ,, ,, ,, (1), , (ii) Find a unit vector â (1), (iii) Write down a unit vector in XY plane, making an angle 60°of with the positive, direction of x – axis. (2), Answer:, (i) (c), Since I = cos π =, 4, , 1, √2, , , m = cos π = 1/2;, 3, , n = cos θ, l2 + m2 + n2 = 1, , https://hssliveguru.com/plus-two-maths-chapter-wise-questions-and-answers-chapter-10/, , 7/19

Page 8 : 12/03/2022, 18:04, , n2 = 1 – ( 12 )2 – (, n=, , 1, 2, , Plus Two Maths Chapter Wise Questions and Answers Chapter 10 Vector Algebra – HSSLive Guru, 1, √2, , )2 = 1/4, , , cosθ = 1/2 , θ =, , π, 3, , ., , (ii), , Question 4., Let the vectors ā, ¯, b, c̄ denoted the sides of a triangle ABC., (i) Prove that (2), (ii) Find the projection of the vector i + 3j + 7k on the vector 7i – j + 8k (2), Answer:, , https://hssliveguru.com/plus-two-maths-chapter-wise-questions-and-answers-chapter-10/, , 8/19

Page 9 : 12/03/2022, 18:04, , Plus Two Maths Chapter Wise Questions and Answers Chapter 10 Vector Algebra – HSSLive Guru, , (ii) Projection of the vector i + 3j + 7k on the vector 7i – j + 8k, , Question 5., (i) If ā and ¯, b are any two vectors, then axb is (1), (a) a vector on the same plane where ā and ¯, b lie., (b) ab cosθ, if θ is the angle between them., (c) a vector parallel to both ā and ¯, b., (d) a vector perpendicular to both ā and ¯, b., (ii) Let ā = 2i + 4j – 5k, ¯, b = i + 2j + 3k. Then find a unit vector perpendicular to both ā, and ¯, b. (2), (iii) Find a vector of magnitude 5 in the direction perpendicular to both ā and ¯, b (1), Answer:, (i) (d) a vector perpendicular to both ā and ¯, b., (ii) ā = 2i + 4j-5k, ¯, b = i + 2j+3k, , = i(12 + 10) – j(6 + 5) + k(4 – 4) = 22i – 11j, , Therefore unit vector perpendicular to both ā and ¯, b is, , (iii) 5 × unit vector perpendicular to both ā and ¯, b, , Question 6., Consider a vector that is inclined at an angle 45° to x-axis and 60° to y-axis, 1. Find the dc’s of the vector. (2), https://hssliveguru.com/plus-two-maths-chapter-wise-questions-and-answers-chapter-10/, , 9/19

Page 10 : 12/03/2022, 18:04, , Plus Two Maths Chapter Wise Questions and Answers Chapter 10 Vector Algebra – HSSLive Guru, , 2. Find a unit vector in the direction of the above vector. (1), 3. Find a vector which is of magnitude 10 units in the direction of the above, vector. (1), Answer:, 1. Let l, m, n are the direction ratios., Given that, l = cos 45° = 1 , m = cos 60° =, √2, , 2, , 2, , 1, 2, , 2, , ⇒l +m +n =1, , ∴ the dc’s of the vector are, , ,, , 1, √2, , 1, 2, , ,, , 1, 2, , 2. A unit vector in the direction of the above vector is given by li + mj + nk ⇒, +, , 1, 2, , 1, √2, , i+, , 1, 2, , j, , k., , 3. A vector, which is of magnitude 10 units in the direction of the above vector is, given by, , Question 7., Consider the point A(2, 1, 1) and B(4, 2, 3), ¯, ¯¯¯¯, ¯¯, ¯, , 1. Find the vector AB (1), ¯, ¯¯¯¯, ¯¯, ¯, , 2. Find the direction cosines of AB (2), ¯, ¯¯¯¯, ¯¯, ¯, , 3. Find the angle made by AB with the positive direction of x-axis. (1), Answer:, ¯, ¯¯¯¯, ¯¯, ¯, , 1. AB = 2i + j + 2k, −, −, −, −, −−, −, −, , ¯, ¯¯¯¯, ¯¯, ¯, , 2. |AB| = √4 + 1 + 4 = 3, The direction cosines are 23 ,, 3. cos α =, , 2, 3, , 1, 3, , ,, , 2, 3, , ., , ⇒ α = cos-1( 23 )., , https://hssliveguru.com/plus-two-maths-chapter-wise-questions-and-answers-chapter-10/, , 10/19

Page 11 : 12/03/2022, 18:04, , Plus Two Maths Chapter Wise Questions and Answers Chapter 10 Vector Algebra – HSSLive Guru, , Question 8., If i + j + k, 2i + 5j, 3i + 2 j – 3k, i – 6j – k respectively are the position vector of points A,, B,C and D. Then, ¯, ¯¯¯¯, ¯¯, ¯, , ¯¯¯¯¯¯¯, ¯, , 1. Find AB and C D. (1), ¯, ¯¯¯¯, ¯¯, ¯, , ¯¯¯¯¯¯¯, ¯, , 2. Find the angle between the vectors AB and C D. (2), ¯, ¯¯¯¯, ¯¯, ¯, , ¯¯¯¯¯¯¯, ¯, , 3. Deduce that AB parallel to C D. (1), Answer:, 1., , 2., , ¯, ¯¯¯¯, ¯¯, ¯, , ¯¯¯¯¯¯¯, ¯, , 3. Since the angle between AB and C D is π they are parallel., , Question 9., Let ABCD be a parallelogram with sides as given in the figure., 1. Find area of the parallelogram. (2), 2. Find the distance between the sides AB and DC. (2), , Answer:, 1. Given;, , https://hssliveguru.com/plus-two-maths-chapter-wise-questions-and-answers-chapter-10/, , 11/19

Page 12 : 12/03/2022, 18:04, ¯, ¯¯¯¯, ¯¯, ¯, , AB, , Plus Two Maths Chapter Wise Questions and Answers Chapter 10 Vector Algebra – HSSLive Guru, ¯, ¯¯¯¯¯¯¯, , = i – 3j + k and AD = i + j + k, , 2. Let h be the distance between the parallelsides AB and DC. Then ; Area = Base × h, _____(2), ¯, ¯¯¯¯, ¯¯, ¯, , Here, Base = |AB|, −, −, −, −, −−, −, −, |i – 3j + k| = √1 + 9 + 1, , −, −, = √11, , From (1) and (2), , Question 10., Consider ā = i + 2j – 3k, ¯, b = 3i – j + 2k, c̄ = 11i + 2j, ¯, 1. Find ā + ¯, b and ā. b (2), , 2. Find the unit vector in the direction of ā + ¯, b. (1), ¯, 3. Show that ā + ¯, b and ā – b are orthogonal. (1), Answer:, , (ii) Unit vector in the direction of, , (iii) We have,, , Therefore, they are orthogonal., , https://hssliveguru.com/plus-two-maths-chapter-wise-questions-and-answers-chapter-10/, , 12/19

Page 13 : 12/03/2022, 18:04, , Plus Two Maths Chapter Wise Questions and Answers Chapter 10 Vector Algebra – HSSLive Guru, , Question 11., Let A (1, -1, 4), B ( 2, 1, 2 ) and C (1, -2, -3 ), ¯, ¯¯¯¯, ¯¯, ¯, , 1. Find AB. (1), ¯, ¯¯¯¯, ¯¯, ¯, , ¯, ¯¯¯¯¯, ¯, ¯, , 2. Find the angle between AB and AC .(2), ¯, ¯¯¯¯, ¯¯, ¯, , ¯, ¯¯¯¯¯, ¯, ¯, , 3. Find the area of the parallelogram formed by AB and AC as adjacent sides., (1), Answer:, ¯, ¯¯¯¯, ¯¯, ¯, , 1. AB = P.v of B – P.v of A, = 2 i + j + 2 k – (i – j + 4k) = i + 2 j – 2k, ¯, ¯¯¯¯¯, ¯, ¯, , 2. AC = P.v of C – P.v of A, = i – 2 j – 3 k -(i – j + 4k) = – j – 7k, ¯, ¯¯¯¯, ¯¯, ¯, , ¯, ¯¯¯¯¯, ¯, ¯, , Let A be the angle between AB and AC, , 3., , Area of the parallelogram, , Plus Two Maths Vector Algebra Six Mark Questions and, Answers, Question 1., Using this figure answer the following questions., , https://hssliveguru.com/plus-two-maths-chapter-wise-questions-and-answers-chapter-10/, , 13/19

Page 14 : 12/03/2022, 18:04, , Plus Two Maths Chapter Wise Questions and Answers Chapter 10 Vector Algebra – HSSLive Guru, , ¯, ¯¯¯¯¯, ¯, ¯ ¯, ¯¯¯¯¯¯, ¯, , ¯, ¯¯¯¯¯¯, ¯, , 1. Find OA, OB, OC (2), ¯¯¯¯¯¯¯, ¯, , 2. Find OD (2), 3. Find the coordinate of the vertex D. (2), Answer:, ¯, ¯¯¯¯¯, ¯, ¯, , 1. OA = (3 – 1)i + (-1 – 2)j + (7 – 3)k = 2i – 3j + 4k, ¯, ¯¯¯¯¯¯, ¯, , = (2 – 1)i + (4 – 2)j +(2 – 3)k = i + 2j – k, , ¯, ¯¯¯¯¯¯, ¯, , = (4 – 1)i + (1 – 2 )j + (5 – 3 )k = 3i – j + 2 k., , OB, OC, , 2. From the figure,, , 3. Let the vertex of D be (x , y , z),, ¯¯¯¯¯¯¯, ¯, , Then, OD = (x – 1)i + (y – 2)j + (z – 3)k., But we have,, ¯¯¯¯¯¯¯, ¯, , OD, , = 6i – 2j + 5k = (x – 1)i + (y – 2)j +(z – 3)k, , x – 1 = 6 ⇒ x = 7, y – 2 = -2 ⇒ y = 0, z – 3 = 5 ⇒ z = 8., , Question 2., OABCDEFG is a cube with edges of length 8 units and axes as shown. L, M, N are, , https://hssliveguru.com/plus-two-maths-chapter-wise-questions-and-answers-chapter-10/, , 14/19

Page 16 : 12/03/2022, 18:04, , Plus Two Maths Chapter Wise Questions and Answers Chapter 10 Vector Algebra – HSSLive Guru, , Question 3., Using the figure answer the following questions, , ¯, ¯¯¯¯, ¯¯, ¯ ¯, ¯¯¯¯¯, ¯, ¯, , 1. Evaluate AB.AC (2), ¯, ¯¯¯¯¯¯¯, , 2. Find AD . (2), 3. Find the coordinates of D., Answer:, ¯, ¯¯¯¯, ¯¯, ¯, , 1. AB = p.v of B – p.v of A= -4i + 0j + 3k, ¯, ¯¯¯¯¯, ¯, ¯, , AC, , = p.v of C – p.v of A = 0i – 4 j + 4k, , ¯, ¯¯¯¯, ¯¯, ¯ ¯, ¯¯¯¯¯, ¯, ¯, , ., , AB AC, , = -4 × 0 + 0 × -4 + 3 × 4 = 12, , 2., , 3. Let the coordinate of D be (x, y ,z), ¯, ¯¯¯¯¯¯¯, , ⇒ AD = (x – 3)i + (y – 2)j + (z – 1)k,, , https://hssliveguru.com/plus-two-maths-chapter-wise-questions-and-answers-chapter-10/, , 16/19

Page 17 : 12/03/2022, 18:04, , Plus Two Maths Chapter Wise Questions and Answers Chapter 10 Vector Algebra – HSSLive Guru, , Question 4., Consider the Parallelogram ABCD, , ¯, ¯¯¯¯, ¯¯, ¯, , ¯, ¯¯¯¯¯¯¯, , 1. Find AB and AD (1), 2. Find the area of the parallelogram ABCD. (1), ¯, ¯¯¯¯¯, ¯, ¯, , 3. Find AC . (2), 4. Find co-ordinate of C. (2), Answer:, ¯, ¯¯¯¯, ¯¯, ¯, , 1. AB = p.v of B – p. v of A, = 3i + 5j + 8k – (i + 2j + k) = 2i + 3j + 7k, ¯, ¯¯¯¯¯¯¯, , AD, , = p.v of D – p. v of A, , = i + 3j + 2k – (i + 2j + k)= 0i + j + k., 2., , 3. By triangle inequality;, , 4. Let the co-ordinate of C be (x, y, z), ¯, ¯¯¯¯¯, ¯, ¯, , Then, AC = (x – 1)i + (y – 2)j + (z – 1)k = 2i + 4j + 8k, x – 1 = 2 ⇒ x = 3, y – 2 = 4 ⇒ y = 6,, z–1=8⇒z=9, Co-ordinate of C is (3, 6, 9)., , https://hssliveguru.com/plus-two-maths-chapter-wise-questions-and-answers-chapter-10/, , 17/19

Page 18 : 12/03/2022, 18:04, , Plus Two Maths Chapter Wise Questions and Answers Chapter 10 Vector Algebra – HSSLive Guru, , Question 5., Consider the following quadrilateral ABCD in which P, Q, R, S are the midpoints of the, sides., , ¯, ¯¯¯¯¯¯, ¯, , ¯¯¯¯¯¯, ¯, , ¯, ¯¯¯¯¯, ¯, ¯, , 1. Find P Q and SR in terms of AC (2), 2. Show that PQRS is a parallelogram. (2), 3. If ā is any vector, prove that (2), , Answer:, 1. Using triangle law of addition, we get, , 2. From the above explanation we have,, , ¯¯¯¯¯¯, ¯, , ¯, ¯¯¯¯¯¯, ¯, , and parallel. Similarly, |SP | = |RQ |, Therefore, PQRS is a parallelogram., 3. Let ā = a1 i + a2 j + a3 k, , Plus Two, Plus One Bussiness Studies Chapter Wise Questions and Answers Chapter 3, Private, Public and Global Enterprises, https://hssliveguru.com/plus-two-maths-chapter-wise-questions-and-answers-chapter-10/, , 18/19

Page 19 : 12/03/2022, 18:04, , Plus Two Maths Chapter Wise Questions and Answers Chapter 10 Vector Algebra – HSSLive Guru, , Plus One Economics Chapter Wise Questions and Answers Chapter 1 Statistics for, Economics Introduction, , Search …, , Recent Posts, HSSLive Plus Two Study Material / Question Bank Kerala, Plus One Malayalam Textbook Answers Unit 4 Chapter 6 Shasthrakriya, Plus One Accountancy Chapter Wise Questions and Answers Kerala, Plus One Economics Chapter Wise Questions and Answers Chapter 4 Presentation of, Data, Kerala Syllabus 9th Standard Maths Solutions Chapter 13 Statistics in Malayalam, Plus One Malayalam Textbook Answers Unit 4 Chapter 5 Samkramanam, Plus One Malayalam Textbook Answers Unit 4 Chapter 4 Vasanavikrithi, Plus One Physics Notes Chapter 5 Law of Motion, Kerala Syllabus 10th Standard Social Science Solutions Chapter 5 Culture and, Nationalism in Malayalam, Plus One Malayalam Textbook Answers Unit 4 Chapter 3 Muhyadheen Mala, Plus One Malayalam Textbook Answers Unit 4 Chapter 2 Anukampa, , Copyright © 2022 HSSLive Guru, , https://hssliveguru.com/plus-two-maths-chapter-wise-questions-and-answers-chapter-10/, , 19/19