The line joining points $(3,5,-7)$ and $(-2,1,8)$ meets yz-plane at point

The line joining points $(3,5,-7)$ and $(-2,1,8)$ meets yz-plane at point
  1. $\left(0, \frac{13}{5}, 2\right)$
  2. $(0,13,2)$
  3. $\left(0, \frac{13}{5},-3\right)$
  4. $\left(0, \frac{-13}{5}, 2\right)$

Solution

Let $\mathrm{y}_{\mathrm{z}}$ plane divides the join in the ratio $\lambda: 1$ then $\frac{\lambda \times(-2)+1 \times 3}{\lambda+1}=0 \Rightarrow \lambda=\frac{3}{2}$ So $\mathrm{y}_{\mathrm{z}}$ plane divides the join in the ratio $3: 2$. Hence, the required point is $\begin{aligned} & \left(\frac{3 \times(-2)+2 \times 3}{3+2}, \frac{3 \times 1+2 \times 5}{3+2}, \frac{3 \times 8+2 \times(-7)}{3+2}\right) \\ & =\left(0, \frac{13}{5}, 2\right)\end{aligned}$

Asked in: MHT CET 2022 (06 Aug Shift 1)

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