Let a=i+2j+k and b=2i+j−k. Let ĉ be a unit... | Vector Algebra

JEE MAIN 2025

08-04-25 S2

Question

Let $\vec{a}=\hat{i}+2 \hat{j}+\hat{k}$ and $\vec{b}=2 \hat{i}+\hat{j}-\hat{k}$. Let $\hat{c}$ be a unit vector in the plane of the vectors $\vec{a}$ and $\vec{b}$ and be perpendicular to $\vec{a}$. Then such a vector $\hat{c}$ is :

Select the correct option:

$\frac{1}{\sqrt{5}}(\hat{j}-2 \hat{k})$

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

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

$\frac{1}{\sqrt{2}}(-\hat{i}+\hat{k})$

✓ Correct! Well done.

✗ Incorrect. Try again or view the solution.

Solution

Question Tags

JEE Main

Mathematics

Medium

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