If two vectors vec P = hati+2 m hatj+m hatk and vecQ=4 hati-2 hatj+m hatk are perpendicular to each other. Then, the value of m will be :

Question

If two vectors vec P = hati+2 m hatj+m hatk and vecQ=4 hati-2 hatj+m hatk are perpendicular to each other. Then, the value of m will be : (A) -1 (B) 2 (C) 3 (D) 1

Tardigrade Admin · Accepted Answer

vecP ⋅ vecQ=0 ( hati+2 m hatj+m hatk) ⋅(4 hati-2 hatj+m hatk)-0 ⇒ 4-4 m+m2=0 ⇒(m-2)2=0 ⇒ m=2

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

-1

2

3

1

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

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 :

-1

2

3

1

P⋅Q​=0 (i^+2mj^​+mk^)⋅(4i^−2j^​+mk^)−0 ⇒4−4m+m2=0 ⇒(m−2)2=0⇒m=2

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

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