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190 Modern College Physics (Mathematical Physicg, Example - ¥2 : By vector method find area of triangle whose vertices are (1, 0, -1), Q,1 Vector Alg, and (0, 1,2). ————, om A eS C(O) Example Answer : AB=i+}j+6k, AC=-i+j+3k, eae 1 i ik Ans, Area of Triangle=—|ABx AC|=—|1 1 6, 2 en B(2,1,5) Example , AC, 05-1), , =5|-31-9}+2k|= 94., , 4, 2, a > = SS 5 > Ans, Example /13 : If A+ B+C=0 prove that [AxB)-(8C|-(€«a)., , Answer: A+B+C=0 = [4 B)--¢, Ang, » Ax{ As B)=-An6 = Axde AnBe CA, = (4 8) =(¢ <A) en ), Also, Bx (A +8)=-Bx€ or BXALBXB=-BxC Se, eePeSCPSAGB=BxC C—O Q, From equationn (1) and (2) we have c i) = ad [B ¢}= = (< x A), Hiss, Psa diagonals of a parallelogram are represented by 3] + i= Ok anda =3) j +4k- (9k, Find its area. Let, > hig . rah hy s 12? three dim, nswer : The.are of a parallelogram with diagonals d; and d, is given by a | dix do]. onde, Sa. i j k m Opa V, : [dxa:)- 3 1 ~2)=-2i-14j-10k je ., = Sir, 1-3 4 :, in the ney, , .. Area of parallelogram, , “basi PRT TF I a