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Q.

If a→ and b→  are the intersecting face diagonals of a cube of side x  in plane XOY  and YOZ,  respectively, with respect to reference frame at the point of intersection of the vectors and sides of cube as the axes, the components of vector r→=a→×b→  are

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a

x,  −x,  x

b

−x2,  −x2,  x2

c

x2,  −x2,x2

d

x,  x2,  −x

answer is C.

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Detailed Solution

Here  a→=xi^+xj^   and b→=xj^+xk^  Since R→ = a→×b→  we get  R→=  |i^j^k^xx00xx|  =  x2i^−x2j^+x2k^Clearly, the components are Rx=x2,  Ry=  −x2,​RZ =x2
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