Question

If the line $\dfrac{x+1}{4} = \dfrac{y+2}{-3} = \dfrac{z-\alpha}{-2}$ passes through the point $(-1,\,-2,\,-3)$, then the value of $\alpha$ is

• A. 4
• B. $-4$
• C. 3
• D. $-3$
• E. $-2$

Hint:

When a specific point is stated to lie on the line, substitute it directly into the symmetric form. All ratios must equal the same value (here 0, since the point IS on the line with parameter $\lambda = 0$ — the point of reference).

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
If a point lies on the line, substituting it into the symmetric form of the line equation must satisfy all three ratios simultaneously.

Step 2: Detailed Explanation:
Substitute $(-1,\,-2,\,-3)$:
\[ \frac{-1+1}{4} = 0, \quad \frac{-2+2}{-3} = 0, \quad \frac{-3-\alpha}{-2} = 0 \] The third ratio gives: $-3 - \alpha = 0 \Rightarrow \alpha = -3$.

Step 3: Final Answer:
$\alpha = -3$.