Question

If $\overline{A}$ $\times$ $\overline{B}$ = $\overline{C}$ then which of the following statements is wrong

• A.
• B.
• C.
• D.

Answer 1

The correct option is D

From the property of vector product, we notice that $\overline{C}$ must be perpendicular to the plane formed by vector$\overline{A}$ and $\overline{B}$. Thus $\overline{C}$
is perpendicular to both $\overline{A}$ and $\overline{B}$ and ($\overline{A}$ + $\overline{B}$) vector also, must lie in the plane formed by vector $\overline{A}$ and $\overline{B}$. Thus $\overline{C}$
must the perpendicular to ($\overline{A}$ +$\overline{B}$ ) also but the cross product ($\overline{A}$ $\times$ $\overline{B}$) gives a vector $\overline{C}$ which can not be perpendicular to
itself. Thus last statement is wrong.