Question

A vector \(\vec{B}\) is along positive y-axis and its vector product with another vector \(\vec{A}\) is zero; then vector \(\vec{A}\) could be

• A. \(5\hat{k}\)
• B. \(5\hat{i}\)
• C. \(5\hat{j}\)
• D. \(-5\hat{k}\)

Hint:

The cross product of two vectors is zero only when they are parallel or antiparallel.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept
The vector product \(\vec{A}\times\vec{B}\) has magnitude \(AB\sin\theta\).
It is zero only when \(\theta = 0^{\circ}\) or \(180^{\circ}\), that is, when the two vectors lie along the same line.

Step 2: Apply to the Given Vectors
\(\vec{B}\) is along the positive y-axis, so \(\vec{A}\) must also lie along the y-axis.

Step 3: Compare the options
Among the options, only \(5\hat{j}\) points along the y-axis.
The vectors \(5\hat{k}\), \(5\hat{i}\) and \(-5\hat{k}\) are perpendicular to \(\hat{j}\), so their cross products with \(\vec{B}\) are not zero.

Final Answer:
The vector \(\vec{A}\) could be \(5\hat{j}\), which is option (C). \[ \boxed{\text{(C) }5\hat{j}} \]