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

Question

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

Infinity Learn · Accepted Answer

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 $$=x2$$

If $\vec{a}$ and $\vec{b}$ are the intersecting face diagonals of a cube of side $x$ in plane $X O Y$ and $Y O Z,$ 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 $\vec{r} = \vec{a} \times \vec{b}$ are

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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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If $\vec{a}$ and $\vec{b}$ are the intersecting face diagonals of a cube of side $x$ in plane $X O Y$ and $Y O Z,$ 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 $\vec{r} = \vec{a} \times \vec{b}$ are