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

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

Solution

Let $\mathrm{A}\left(\mathrm{x}_{1}, \mathrm{y}_{1}, \mathrm{z}_{1}\right)=(3,4,-7)$ $\mathrm{B}\left(\mathrm{x}_{2}, \mathrm{y}_{2}, \mathrm{z}_{2}\right)=(1,-1,6)$ Required equation is $\mathrm{x}=\mathrm{x}_{1}+\lambda\left(\mathrm{x}_{2}-\mathrm{x}_{1}\right) \Rightarrow \mathrm{x}=3-2 \lambda$ $\mathrm{y}=\mathrm{y}_{1}+\lambda\left(\mathrm{y}_{2}-\mathrm{y}_{1}\right) \Rightarrow \mathrm{y}=4-5 \lambda$ $\mathrm{z}=\mathrm{z}_{1}+\lambda\left(\mathrm{z}_{2}-\mathrm{z}_{1}\right) \Rightarrow \mathrm{z}=-7+13 \lambda$

Asked in: MHT CET 2020 (12 Oct Shift 1)

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