Question

A line drawn from a point $A(-2,-2,3)$ and parallel to the line $\frac{x}{-2} = \frac{y}{2} = \frac{z}{-1}$ meets the $YOZ$ plane in point $P$, then the coordinates of the point $P$ are

• A. $(0, 4, -4)$
• B. $(0, 2, 2)$
• C. $(0, -2, 2)$
• D. $(0, -4, 4)$

Hint:

Any point on the $YOZ$ plane must have an $x$-coordinate of 0, which all options correctly show. Next, examine the direction ratios: for every change of $+2$ units along $x$ (moving from $-2$ to $0$), $y$ must change by $-2$ units (based on the ratio $\frac{\Delta x}{-2} = \frac{\Delta y}{2}$). Thus, $y = -2 - 2 = -4$, isolating option (D) instantly without full calculation!

Answer 1

The Correct Option is D

Step 1: Understanding the Question:
Find point P where a line through A(–2,–2,3) parallel to direction (–2,2,–1) meets the YOZ plane.

Step 2: Key Formula or Approach:
Parametric form: x = –2λ–2, y = 2λ–2, z = –λ+3. On YOZ plane, x = 0.

Step 3: Detailed Explanation:
Set x=0 → –2λ–2=0 → λ=–1. Then y=2(–1)–2=–4; z=–(–1)+3=4. Point P is (0,–4,4).

Step 4: Final Answer:
The coordinates are (0,–4,4), matching option (D).