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

Given: a = i + 2 j + k and b = 2 i + j - k. We need a unit vector c that lies in the plane of a and b and is perpendicular to a. Find: The correct option representing c. The solution could not be extracted, so the answer is resolved from the provided correct answer field if available. For this record, the extracted answer is B.

Let a = i + 2 j + k and b = 2 i + j - k. Let c be a unit vector i… — Solution | JEE Mathematics

MCQMediumJEE 2025Basics of Vectors

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 perpendicular to $\vec{a}$ . Then such a vector $\hat{c}$ is:

A
$\frac{1}{\sqrt{3}} (\hat{i} - \hat{j} + \hat{k})$
B
$\frac{1}{\sqrt{2}} (-\hat{i} + \hat{k})$
C
$\frac{1}{\sqrt{5}} (\hat{j} - 2\hat{k})$
D
$\frac{1}{\sqrt{3}} (-\hat{i} + \hat{j} - \hat{k})$

Answer

Correct answer:B

Step-by-step solution

the solution unavailable

Given: $\vec{a} = \hat{i} + 2 \hat{j} + \hat{k}$ and $\vec{b} = 2 \hat{i} + \hat{j} - \hat{k}$ . We need a unit vector $\hat{c}$ that lies in the plane of $\vec{a}$ and $\vec{b}$ and is perpendicular to $\vec{a}$ .

Find: The correct option representing $\hat{c}$ .

The solution could not be extracted, so the answer is resolved from the provided correct answer field if available. For this record, the extracted answer is B.

Common mistakes

Choosing a vector only perpendicular to $\vec{a}$ but not checking whether it lies in the plane of $\vec{a}$ and $\vec{b}$ . Both conditions must be satisfied.
Checking orthogonality but forgetting the unit-vector condition. After finding a perpendicular direction, its magnitude must be normalized to $1$ .
Using $\vec{a} \times \vec{b}$ directly. That vector is perpendicular to the plane of $\vec{a}$ and $\vec{b}$ , whereas $\hat{c}$ must lie inside that plane.

Practice more Basics of Vectors questions

Get unlimited AI-adaptive practice, mastery tracking, and an AI tutor that explains every step — free to start.

Start free trial More on Basics of Vectors

Answer

Step-by-step solution

Common mistakes

Practice more Basics of Vectors questions

Related questions