Question

If the vectors $\overrightarrow{A}=a\hat{i}+\hat{j}-2\hat{k}$ and $\hat{B}=a\hat{i}-a\hat{j}+\hat{k}$ are perpendicular to each other then the positive value then the positive value of 'a' is

• A. Zero
• B. 1
• C. -1
• D. 3

Answer 1

The correct option is C -1

Vectors : $\overrightarrow{A}=a\hat{i}+\hat{j}-2\hat{k},\overrightarrow{B}=a\hat{i}-a\hat{j}+\hat{k}$

$\overrightarrow{A}$ & $\overrightarrow{B}$ are perpendicular when, $\overrightarrow{A}.\overrightarrow{B}=0$

$\overrightarrow{A}.\overrightarrow{B}=(a\hat{i}+\hat{j}-2\hat{k}).(a\hat{i}-a\hat{j}+\hat{k})=a^2-a-2=0$

$\Rightarrow (a-2)(a+1)=0\Rightarrow a=2$ or $a=-1$