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Question

Find the values of x and y if the vectors a =3i^+xj^-k^ and b =2i^+j^+yk^ are mutually perpendicular vectors of equal magnitude.

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Solution

We havea=3i^+xj^-k^ and b=2i^+j^+yk^It is given that the vectors are perpendicular.a. b=06+x-y=0x-y=-6 ... 1Also, it is given thata=b9+x2+1=4+1+y210+x2=5+y2 10+x2=5+y2 x2-y2=-5x+yx-y=-5-6 x+y=-5 Using 1x+y=56 ... 2(1)+(2) gives2x=-316x=-3112From (1),-3112-y=-6y=-3112+6=4112x=-3112 and y=4112

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