Question

A vector \( \mathbf{P} \) has components along X and Y axis having magnitude 2 units and 4 units respectively. A vector along negative X-axis, \( \mathbf{Q} \) has magnitude 6 units. Then vector \( (\mathbf{P} - \mathbf{Q}) \) is:

• A. \( 4 (2 \hat{i} + \hat{j}) \)
• B. \( -4 (2 \hat{i} - \hat{j}) \)
• C. \( 4 (2 \hat{i} - \hat{j}) \)
• D. \( -4 (2 \hat{i} + \hat{j}) \)

Hint:

When subtracting vectors, subtract their corresponding components along each axis.

Answer 1

The Correct Option is C

Step 1: Vector Components.
The vector \( \mathbf{P} \) has components \( 2 \hat{i} + 4 \hat{j} \). The vector \( \mathbf{Q} \) is along the negative X-axis, so its components are \( -6 \hat{i} \). To find \( \mathbf{P} - \mathbf{Q} \), subtract the components: \[ \mathbf{P} - \mathbf{Q} = (2 \hat{i} + 4 \hat{j}) - (-6 \hat{i}) = 2 \hat{i} + 4 \hat{j} + 6 \hat{i} = 8 \hat{i} + 4 \hat{j} \] Thus, the resulting vector is \( 4 (2 \hat{i} - \hat{j}) \).
Step 2: Final Answer.
Thus, \( \mathbf{P} - \mathbf{Q} = 4 (2 \hat{i} - \hat{j}) \).