Question

$A$ and $B$ are two perpendicular vectors given by $\overrightarrow{A}=5\hat{i}+10\hat{j}-3\hat{k}$ and $\overrightarrow{B}=2\hat{i}+4\hat{j}-c\hat{k}$. The value of $c$ is:

• A. $1/6$
• B. $3/2$
• C. $5/6$
• D. $-50/3$

Answer 1

The correct option is D $-50/3$

$Let,d=\overrightarrow{A}\cdot \overrightarrow{B}\overrightarrow{A}\perp \overrightarrow{B}\Rightarrow d=0\overrightarrow{A}=5\hat{i}+10\hat{j}-3\hat{k}\overrightarrow{B}=2\hat{i}+4\hat{j}-c\hat{k}\Rightarrow d=5\times 2+10\times 4+(-3)\times (-c)=0\Rightarrow 3c=-50\Rightarrow c=\frac{-50}{3}$