Question

Assertion :Vector $\overrightarrow{c}=-5\hat{i}+7\hat{j}+2\hat{k}$ is along the bisector of angle between $\overrightarrow{a}=\hat{i}+2\hat{j}+2\hat{k}$ and $\overrightarrow{b}=-8\hat{i}+\hat{j}-4\hat{k}.$ Reason: $\overrightarrow{c}$ is equally inclined to $\overrightarrow{a}$ and $\overrightarrow{b}$.

• A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
• C. Assertion is correct but Reason is incorrect
• D. Assertion is incorrect but Reason is correct

Answer 1

The correct option is A Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

A vector along the bisector is
$\frac{\overrightarrow{a}}{|\overrightarrow{a}|}+\frac{\overrightarrow{b}}{|\overrightarrow{b}|}=\frac{-5\hat{i}+7\hat{j}+2\hat{k}}{9}$

Hence $\overrightarrow{c}=-5\hat{i}+7\hat{j}+2\hat{k}$ is along the bisector. It is obvious that $\overrightarrow{c}$ makes an equal angle with $\overrightarrow{a}$ and $\overrightarrow{b}$. However, Reason does not explain assertion as a vector equally inclined to given two vector is not necessarily coplanar.