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

JEE Main · 2023 · 24 Jan 2023 · Shift 2 · Vector

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 :

Answer: (D)

Two vectors are perpendicular when their scalar product vanishes. Here

P \cdot Q = (1) (4) + (2 m) (- 2) + (m) (m) = 4 - 4 m + m^{2}

. Setting this equal to zero gives

m^{2} - 4 m + 4 = 0

, that is

(m - 2)^{2} = 0

. The value of

m

2

JEE Main · 2023 · 24 Jan 2023 · Shift 2 · Single correct option