Question

The unit vector along the mutually perpendicular x , y and z axes are $\hat{i},\hat{j}and\hat{k}$ respectively . Consider the plane z = 0 and two vectors $\overrightarrow{a}$ and $\overrightarrow{b}$ on that plane. Such that $\overrightarrow{a}\ne \alpha \overrightarrow{b}$ for any scalar $\alpha$. A vector perpendicular to both
$\overrightarrow{a}$ and $\overrightarrow{b}$ is

• A. $-\hat{j}$
• B. $\hat{i}$
• C. $\hat{k}$
• D. $\hat{i}-\hat{j}$

Answer 1

The correct option is C $\hat{k}$

(c)
Given, z =0 and $\overrightarrow{a}\ne \alpha \overrightarrow{b}$

So, it is clear that both $\overrightarrow{a},\overrightarrow{b}$ are in x-y plane.
$\therefore$ The vector perpendicular to both $\overrightarrow{a},\overrightarrow{b}$ will be in the direction of z-axis.