If two vectors and are perpendicular to each other. Then, the value of m will be [2023]

Question

If two vectors $\vec{P} = \hat{i} + 2 m \hat{j} + m \hat{k}$ and $\vec{Q} = 4 \hat{i} - 2 \hat{j} + m \hat{k}$ are perpendicular to each other. Then, the value of m will be [2023]

Smart Achievers · Accepted Answer

(2)

$\vec{P} \cdot \vec{Q} = 0$

$(\hat{i} + 2 m \hat{j} + m \hat{k}) \cdot (4 \hat{i} - 2 \hat{j} + m \hat{k}) = 0 \Rightarrow 4 - 4 m + m^{2} = 0$

$\Rightarrow {(m - 2)}^{2} = 0 \Rightarrow m = 2$

Solution

Q.
If two vectors $\vec{P} = \hat{i} + 2 m \hat{j} + m \hat{k}$ and $\vec{Q} = 4 \hat{i} - 2 \hat{j} + m \hat{k}$ are perpendicular to each other. Then, the value of m will be [2023]

1 –1

2 2

3 3

4 1

Ans.
(2)

$\vec{P} \cdot \vec{Q} = 0$

$(\hat{i} + 2 m \hat{j} + m \hat{k}) \cdot (4 \hat{i} - 2 \hat{j} + m \hat{k}) = 0 \Rightarrow 4 - 4 m + m^{2} = 0$

$\Rightarrow {(m - 2)}^{2} = 0 \Rightarrow m = 2$

Want Us to Email you About Special Offers & Updates?

Solution

Q. If two vectors P→=i^+2mj^+mk^ and Q→=4i^–2j^+mk^ are perpendicular to each other. Then, the value of m will be [2023]

1 –1

2 2

3 3

4 1

Ans. (2) P→·Q→=0 (i^+2mj^+mk^)·(4i^–2j^+mk^)=0 ⇒ 4–4m+m2=0 ⇒ (m–2)2=0 ⇒ m=2

Want Us to Email you About Special Offers & Updates?

Q.
If two vectors $\vec{P} = \hat{i} + 2 m \hat{j} + m \hat{k}$ and $\vec{Q} = 4 \hat{i} - 2 \hat{j} + m \hat{k}$ are perpendicular to each other. Then, the value of m will be [2023]

Ans.
(2)

$\vec{P} \cdot \vec{Q} = 0$

$(\hat{i} + 2 m \hat{j} + m \hat{k}) \cdot (4 \hat{i} - 2 \hat{j} + m \hat{k}) = 0 \Rightarrow 4 - 4 m + m^{2} = 0$

$\Rightarrow {(m - 2)}^{2} = 0 \Rightarrow m = 2$