Q152 / 200 · MHT CET - Medical 2026 (23 April Shift 1) · Physics
Given $\vec{A} = 2\hat{i} - 2\hat{j} + 8\hat{k}$ and $\vec{B} = 2\hat{i} - m\hat{j} + 8\hat{k}$, if $\vec{A}$ and $\vec{B}$ have the same direction, the value of $m$ is
- A$1$
- Correct answerB$2$
- C$3$
- D$4$
Solution
For two vectors $\vec{A}$ and $\vec{B}$ to have the same direction, their corresponding components must be proportional with a positive ratio.
$\dfrac{A_x}{B_x} = \dfrac{A_y}{B_y} = \dfrac{A_z}{B_z}$
Substituting the given values:
$\dfrac{2}{2} = \dfrac{-2}{-m} = \dfrac{8}{8}$
$1 = \dfrac{2}{m} = 1$
$m = 2$
Answer: $2$
$\dfrac{A_x}{B_x} = \dfrac{A_y}{B_y} = \dfrac{A_z}{B_z}$
Substituting the given values:
$\dfrac{2}{2} = \dfrac{-2}{-m} = \dfrac{8}{8}$
$1 = \dfrac{2}{m} = 1$
$m = 2$
Answer: $2$
Hence, the correct answer is option: 'B'.