Question

If $\overset{\rightarrow}{A} \times \overset{\rightarrow}{B} = \overset{\rightarrow}{C},$ then which of the following statements is wrong-

• A. $\overset{\rightarrow}{C}\bot\overset{\rightarrow}{A}$
• B. $\overset{\rightarrow}{C}\bot\overset{\rightarrow}{B}$
• C. $\overset{\rightarrow}{C}\bot(\overset{\rightarrow}{A} + \overset{\rightarrow}{B})$
• D. $\overset{\rightarrow}{C}\bot(\overset{\rightarrow}{A} \times \overset{\rightarrow}{B})$

Answer 1

Answer: (D)

$\overset{\rightarrow}{C}\bot(\overset{\rightarrow}{A} \times \overset{\rightarrow}{B})$

Answer 2

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