Question

If $\overrightarrow{A}$ and $\overrightarrow{B}$ are perpendicular vectors and vector $\overrightarrow{A} = 5\widehat{i} + 7\widehat{j} - 3\widehat{k}$ and $\overrightarrow{B} = 2\widehat{i} + 2\widehat{j} - a\widehat{k}.$ The value of a is

• A. – 2
• B. 8
• C. – 7
• D. – 8

Answer 1

Answer: (D)

– 8

Answer 2

For perpendicular vector $\overset{\rightarrow}{A}.\overset{\rightarrow}{B} = 0$

⇒ $(5\widehat{i} + 7\widehat{j} - 3\widehat{k}).(2\widehat{i} + 2\widehat{j} - a\widehat{k}) = 0$

⇒ $10 + 14 + 3a = 0 \Rightarrow$ $a = - 8$