Q152 / 200 · MHT CET - Medical 2026 (24 April Shift 2) · Physics
What is the relation between the two vectors $\vec{A} = 2\hat{i} + 5\hat{j} - 6\hat{k}$ and $\vec{B} = \hat{i} + \dfrac{5}{2}\hat{j} - 3\hat{k}$ ?
- A$\vec{A}$ is perpendicular to $\vec{B}$
- Correct answerB$\vec{A}$ is parallel to $\vec{B}$
- C$\vec{A} + \vec{B} = 0$
- D$\vec{A} - \vec{B} = 0$
Solution
Given vectors are $\vec{A} = 2\hat{i} + 5\hat{j} - 6\hat{k}$ and $\vec{B} = \hat{i} + \dfrac{5}{2}\hat{j} - 3\hat{k}$.
Taking $2$ common from the components of $\vec{A}$:
$\vec{A} = 2(\hat{i} + \dfrac{5}{2}\hat{j} - 3\hat{k})$
$\vec{A} = 2\vec{B}$
Since $\vec{A}$ is a scalar multiple of $\vec{B}$, the two vectors are parallel.
Answer: $\vec{A}$ is parallel to $\vec{B}$
Taking $2$ common from the components of $\vec{A}$:
$\vec{A} = 2(\hat{i} + \dfrac{5}{2}\hat{j} - 3\hat{k})$
$\vec{A} = 2\vec{B}$
Since $\vec{A}$ is a scalar multiple of $\vec{B}$, the two vectors are parallel.
Answer: $\vec{A}$ is parallel to $\vec{B}$
Hence, the correct answer is option: 'B'.