Question

If the vectors \( \hat{i} + 2\hat{j} + \hat{k} \) and \( \hat{i} + 6\hat{j} + 4\hat{k} \) are collinear, then the values of \( x \) and \( y \) are respectively

• A. \( \frac{4}{3}, 3 \)
• B. 3, 4
• C. \( \frac{1}{3}, 1 \)
• D. 4, 3

Hint:

For collinear vectors, express one vector as a scalar multiple of the other and solve for the unknowns.

Answer 1

The Correct Option is A

Step 1: Condition for collinearity.
Two vectors are collinear if one is a scalar multiple of the other. Hence, for the given vectors \( \hat{i} + 2\hat{j} + \hat{k} \) and \( \hat{i} + 6\hat{j} + 4\hat{k} \), we set up the following equation: \[ x(\hat{i} + 2\hat{j} + \hat{k}) = \hat{i} + 6\hat{j} + 4\hat{k} \]
Step 2: Solve for \( x \) and \( y \).
Solving this equation, we find \( x = \frac{4}{3} \) and \( y = 3 \), corresponding to option (A).