Question

The co-ordinates of the point where the line joining the points \((3,5,-7)\) and \((-2,1,8)\) is intersected by the YOZ plane are

• A. \((0,\frac{-13}{5},\frac{2}{5})\)
• B. \((0,\frac{13}{5},\frac{2}{5})\)
• C. \((0,\frac{13}{5},2)\)
• D. \((0,\frac{-13}{5},-2)\)

Hint:

On the YOZ plane x = 0; write the line in parametric form and find the parameter.

Answer 1

The Correct Option is C

Step 1: Section formula view
The plane $x = 0$ divides the segment in the ratio $3 : 2$ (distances 3 and 2 from the x values 3 and $-2$), internally.

Step 2: Coordinates
$y = \dfrac{3\cdot1 + 2\cdot5}{5} = \dfrac{13}{5}$ and $z = \dfrac{3\cdot 8 + 2\cdot(-7)}{5} = \dfrac{10}{5} = 2$.

Step 3: Point
$(0, 13/5, 2)$, option (C).

Final Answer:
Option (C). \[ \boxed{\left(0,\frac{13}{5},2\right)} \]