Question

equals to 3 ICAP - 2 J cap + K cap is perpendicular to vector Q is equals to two ICAP + 3 J cap - K cap what is value of a=?​

Answer 1

Answer: 3)4

Explanation:

As they are perpendicular, theta is 90°

We know that

p.q cos theta = n

As cos theta =0,

n=0

=> (3i-2j+ak).(2i+j-k)=0

=> 3*2-2*1-1*a=0

=> 6-2-a=0

=> a=4

Answer 2

The value of a = 4

Correct question : A vector $\vec{P} = 3 \hat{i} - 2\hat{j} + a\hat{ k}$ is perpendicular to the vector $\vec{Q} = 2 \hat{i} + \hat{j} - \hat{ k}$. Then value of a is 1) 2 2) 1 3) 4 4) 3

Given :

A vector $\vec{P} = 3 \hat{i} - 2\hat{j} + a\hat{ k}$ is perpendicular to the vector $\vec{Q} = 2 \hat{i} + \hat{j} - \hat{ k}$

To find :

The value of a is

1) 2

2) 1

3) 4

4) 3

Solution :

Step 1 of 2 :

Write down the given vectors

Here the given vectors are

$\vec{P} = 3 \hat{i} - 2\hat{j} + a\hat{ k}$

$\vec{Q} = 2 \hat{i} + \hat{j} - \hat{ k}$

Step 2 of 2 :

Find the value of a

Here it is given that the vector $\vec{P} = 3 \hat{i} - 2\hat{j} + a\hat{ k}$ is perpendicular to the vector $\vec{Q} = 2 \hat{i} + \hat{j} - \hat{ k}$

∴ Dot product of two vectors = 0

$\displaystyle{ \implies }\vec{P}.\vec{Q} = 0$

$\implies (3 \hat{i} - 2\hat{j} + a\hat{ k}).( 2 \hat{i} + \hat{j} - \hat{ k}) = 0$

$\implies (3.2) + ( - 2.1) + (a. - 1) = 0$

$\implies 6 - 2 - a = 0$

$\implies 4 - a = 0$

$\implies a = 4$

Hence the correct option is 3) 4

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