#### Need solution for rd sharma maths class 12 chapter 24 vector or cross product Exercises Multiple choice questions question 8 maths textbook solution

Answer $\frac{1}{\sqrt{3}}\left ( \hat{i}-\hat{j}+\hat{k} \right )$

Given: A unit vector perpendicular to both $\hat{i}+\hat{j}$ and $\hat{j}+\hat{k}$

Hint: You must know about cross product

Explanation:  Let $\overrightarrow{a}=\hat{i}+\hat{j}$;$\overrightarrow{b}=\hat{j}+\hat{k}$

A unit vector perpendicular to both $\frac{\overrightarrow{a}\times \overrightarrow{b}}{\left | \overrightarrow{a}\times \overrightarrow{b} \right |}$

Now,

\begin{aligned} &\vec{a} \times \vec{b}=\left|\begin{array}{ccc} \hat{i} & \hat{j} & \hat{k} \\ 1 & 1 & 0 \\ 0 & 1 & 1 \end{array}\right| \\ &=\hat{i}(1-0)-\hat{j}(1-0)+\hat{k}(1-0) \\ &= & \hat{i}-\hat{j}+\hat{k} \\ &|\vec{a} \times \vec{b}|=\sqrt{(1)^{2}+(-1)^{2}+(1)^{2}}=\sqrt{3} \\ &\therefore \text { Unit vector }=\frac{\hat{i}-\hat{j}+\hat{k}}{\sqrt{3}} \\ & \end{aligned}

$=\frac{1}{\sqrt{3}}(\hat{i}-\hat{j}+\hat{k})$