Question

If the vectors \( (2\mathbf{i}-q\mathbf{j}+3\mathbf{k}) \) and \( (4\mathbf{i}-5\mathbf{j}+6\mathbf{k}) \) are collinear, then the value of \( q \) is

• A. \( \dfrac{5}{2} \)
• B. \( -\dfrac{5}{2} \)
• C. \( -\dfrac{2}{5} \)
• D. \( \dfrac{2}{5} \)

Hint:

For collinear vectors, ratios of corresponding components must be equal.

Answer 1

The Correct Option is A

Step 1: Use the condition for collinearity.
If two vectors are collinear, then their corresponding components are proportional.
Step 2: Form ratios.
\[ \frac{2}{4} = \frac{-q}{-5} = \frac{3}{6} \] Step 3: Simplify the ratios.
\[ \frac{1}{2} = \frac{q}{5} \] Step 4: Solve for \( q \).
\[ q = \frac{5}{2} \] Step 5: Conclusion.
The value of \( q \) is \( \dfrac{5}{2} \).