The parametric equations of a line passing through the points $\mathrm{A}$ $(3,4,-7)$ and $B(1,-1,6)$ are

The parametric equations of a line passing through the points $\mathrm{A}$ $(3,4,-7)$ and $B(1,-1,6)$ are
  1. $\mathrm{x}=3+\lambda, \mathrm{y}=-1+4 \lambda, \mathrm{z}=-7+6 \lambda$
  2. $\mathrm{x}=-2+3 \lambda, \mathrm{y}=-5+4 \lambda, \mathrm{z}=13-7 \lambda$
  3. $\mathrm{x}=3+2 \lambda, \mathrm{y}=4-5 \lambda, \mathrm{z}=-7-13 \lambda$
  4. $\mathrm{x}=3-2 \lambda, \mathrm{y}=4-5 \lambda, \mathrm{z}=-7+13 \lambda$

Solution

Equation of required line is $\begin{aligned} & \frac{x-3}{1-3}=\frac{y-4}{-1-4}=\frac{z+7}{6+7}=\lambda \ldots \text { (Say) } \\ & \therefore \frac{x-3}{-2}=\frac{y-4}{-5}=\frac{z+7}{13}=\lambda \\ & \therefore x=-2 \lambda+3, y=-5 \lambda+4, z=13 \lambda-7 \end{aligned}$

Asked in: MHT CET 2021 (20 Sep Shift 1)

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