The unit vector perpendicular to each of the vectors a+b and a-b, where a=i+j+k and b=i+2 j+3 k, is : Option 1: 1sqrt(6) i+2sqrt(6) j+1sqrt(6) k Option 2: -1sqrt(6) i+1sqrt(6) j-1sqrt(6) k Option 3: -1sqrt(6) i+2sqrt(6) j+2sqrt(6) k Option 4: -1sqrt(6) i+2sqrt(6) j-1sqrt(6) k

The answer is '-1sqrt(6) i+2sqrt(6) j-1sqrt(6) k'. View full solution:

The unit vector perpendicular to each of the vectors a+b and a-b, where a=i+j+k and b=i+2 j+3 k, is :

-1sqrt(6) i+2sqrt(6) j-1sqrt(6) k

1sqrt(6) i+2sqrt(6) j+1sqrt(6) k

-1sqrt(6) i+1sqrt(6) j-1sqrt(6) k

-1sqrt(6) i+2sqrt(6) j+2sqrt(6) k

-1sqrt(6) i+2sqrt(6) j-1sqrt(6) k

Algebra > Vector Algebra

Medium

core

The unit vector perpendicular to each of the vectors $\vec{a}+\vec{b}$ and $\vec{a}-\vec{b}$, where $\vec{a}=\hat{i}+\hat{j}+\hat{k}$ and $\vec{b}=\hat{i}+2 \hat{j}+3 \hat{k}$, is :

$\frac{1}{\sqrt{6}} \hat{i}+\frac{2}{\sqrt{6}} \hat{\mathrm{j}}+\frac{1}{\sqrt{6}} \hat{\mathrm{k}}$

$-\frac{1}{\sqrt{6}} \hat{\mathrm{i}}+\frac{1}{\sqrt{6}} \hat{\mathrm{j}}-\frac{1}{\sqrt{6}} \hat{\mathrm{k}}$

$-\frac{1}{\sqrt{6}} \hat{\mathrm{i}}+\frac{2}{\sqrt{6}} \hat{\mathrm{j}}+\frac{2}{\sqrt{6}} \hat{\mathrm{k}}$

$-\frac{1}{\sqrt{6}} \hat{\mathrm{i}}+\frac{2}{\sqrt{6}} \hat{\mathrm{j}}-\frac{1}{\sqrt{6}} \hat{\mathrm{k}}$

✅ Correct Option: 4

Related questions:

2025: 15 May Shift 2

If $\hat{a}, \hat{b}$ and $\hat{c}$ are three unit vectors and $\hat{a} + \hat{b} + \hat{c} = \vec{0}$ , then the angle between $\hat{a}$ and $(-\hat{b})$ is

2022: 23 Aug Shift 1

A vector perpendicular to a plane containing a triangle ABC having vertices as $A(1,1,0)$ , $B(2,1,1)$ and $C(0,3,2)$ , is:

2026: 26th May Shift 2

If $\hat{i}, \hat{j}, \hat{k}$ represents unit vectors along x, y, z axes respectively, then

Match List-I with List-II

LIST-I		LIST-II
A.	$\hat{i}.\hat{i}$	I. 0
B.	$\hat{i}.\hat{j}$	II. $\vec{0}$
C.	$\hat{i} \times \hat{j}$	III. 1
D.	$\hat{i} \times \hat{i}$	IV. $\hat{k}$

Choose the correct answer from the options given below:

2025: 21 May Shift 2

The vector in the direction of the vector $2\hat{i} - \hat{j} - 2\hat{k}$ that has magnitude 9 units is:

2025: 27 May Shift 1

The projection of the vector $5\hat{i} + \hat{j} - 3\hat{k}$ on the vector $\hat{i} + 2\hat{j} - 3\hat{k}$ is

2024: 16 May Shift 1

Which of the following cannot be the direction ratios of the straight line $\frac{x-3}{2}=\frac{2-y}{3}=\frac{z+4}{-1}$ ?

The unit vector perpendicular to each of the vectors $\vec{a}+\vec{b}$ and $\vec{a}-\vec{b}$, where $\vec{a}=\hat{i}+\hat{j}+\hat{k}$ and $\vec{b}=\hat{i}+2 \hat{j}+3 \hat{k}$, is :

Keyboard Shortcuts