Question 3 :
Let a,b be two noncoffinear vectors. If $\overline { OA } =\left( x+4y \right) \overline { a } +\left( 2x+y+1 \right) \overline { b } ,\overline { OB } =\left( y-2x+2 \right) \overline { a } +\left( 2x-3y-1 \right) \overline { b }$ and $3\overline { OA } =2\overline { OB }, $ then $\left( x,y \right) =$

Question 4 :
Consider two vectors $\vec{F_{1}}=2\hat{i}+5\hat{k}$ and $\vec{F_{2}}=3\hat{j}+4\hat{k}$. The magnitude of the scalar product of these vectors is

Question 5 :
When a body is thrown up, the sign of $g$ is positive when it goes up.

Question 6 :
If $\lambda (2\overline {i} - 4\overline {j} + 4\overline {k})$ is a unit vector then $\lambda =$

Question 7 :
If $\vec{a}, \vec{b}, \vec{c}$ are three non coplanar vectors, then $(\vec{a}+\vec{b}+\vec{c})[(\vec{a}+\vec{b}) \times (\vec{a}+\vec{c})] $ is :

Question 8 :
If the position vectors of the points $A, B, C, D$ are$(0,2, 1)$, $(3,1,1),$ $(-5,3,2)$,$(2,4,1)$ respectively and if $PA+PB+PC+PD=0$ then the position vector of P is<br/>

Question 9 :
Two vectors $a$ and $b$ are said to be equal, if <br>I. $|a| = |b|$<br>II. they have same or parallel support.<br>III. the same sense.<br>Which of the following is true?

Question 10 :
If $\left| {\vec a} \right| = 2,\left| {\vec b} \right| = 3$ and $\left| {2\vec a - \vec b} \right| = 5,$ then $\left| {2\vec a + \vec b} \right|$ equals:

Question 12 :
Direction angle of a vector is $30^{o}$, then find the vector.

Question 14 :
$\vec{a},\vec{b},\vec{c}$ are three non-collinear vectors such that $\vec{a}+\vec{b}$ is parallel to $\vec{c}$ and $\vec{a}+\vec{c}$ is parallel to $\vec{b}$ then:

Question 15 :
If $\left[ \overrightarrow { a } \overrightarrow { b } \overrightarrow { c } \right] =1$ then $\frac { \overrightarrow { a } .\overrightarrow { b }\times \overrightarrow { c } }{ \overrightarrow { c }\times \overrightarrow { a } .\overrightarrow { b } } +\frac { \overrightarrow { b } .\overrightarrow { c }\times \overrightarrow { a } }{ \overrightarrow { a }\times \overrightarrow { b } .\overrightarrow { c } } +\frac { \overrightarrow { c } .\overrightarrow { a }\times \overrightarrow { b } }{ \overrightarrow { b }\times \overrightarrow { c } .\overrightarrow { a } }$ <span>is equal to</span>

Question 17 :
Let $a=\hat{i}+2\hat j+3\hat k$ and $b=3\hat i+\hat j$. Find the unit vector in the direction of the $a+b$.

Question 18 :
For $O$ being the origin and $3$ points $P,Q$ and $R$ lie on a plane. If $\displaystyle \vec{PO}+\vec{OQ}=\vec{QO}+\vec{OR}$, then $P, Q, R$ are <br/>

Question 20 :
Given $\vec p= (2,-4,1), \vec q = (3,-1,2), \vec r = (5,5, 4)$. Then $\vec{PQ}$ and $\vec{QR}$ are