The Cartesian equation of the line passing through the point $(-3,0,1)$ and perpendicular to vectors…

The Cartesian equation of the line passing through the point $(-3,0,1)$ and perpendicular to vectors $\hat{i}-2 \widehat{j}+\widehat{k}$ and $2 \hat{i}+\widehat{j}-\widehat{k}$ is
  1. $\frac{x+3}{1}=\frac{y}{3}=\frac{z-1}{-5}$
  2. $\frac{x+3}{-1}=\frac{y}{3}=\frac{z-1}{5}$
  3. $\frac{x+3}{1}=\frac{y}{3}=\frac{z-1}{5}$
  4. $\frac{x+3}{1}=\frac{y}{-3}=\frac{z-1}{5}$

Solution

$\begin{aligned} & \frac{\mathrm{x}+3}{(-2) \times(-1)-1 \times 1}=\frac{\mathrm{y}-0}{2 \times 1-1 \times(-1)}=\frac{\mathrm{z}-1}{1 \times 1-2 \times(-2)} \\ & \Rightarrow \frac{\mathrm{x}+3}{1}=\frac{\mathrm{y}}{3}=\frac{\mathrm{z}-1}{5}\end{aligned}$

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

Practice more Line and Plane questions on Aicharya