Q61 / 180 · KCET 2021 · Mathematics

The equation of the line joining the points $(-3,4,11)$ and $(1,-2,7)$ is

  • A
    $\frac{x+3}{2}=\frac{y-4}{3}=\frac{z-11}{4}$
  • Correct answer
    B
    $\frac{x+3}{-2}=\frac{y-4}{3}=\frac{z-11}{2}$
  • C
    $\frac{x+3}{-2}=\frac{y+4}{3}=\frac{z+11}{4}$
  • D
    $\frac{x+3}{2}=\frac{y+4}{-3}=\frac{z+11}{2}$

Solution

Given, points are $(-3,4,11)$ and $(1,-2,7)$. Let $A(-3,4,11)$ and $B(1,-2,7)$ Direction ratios of $A B=1-(-3),-2-4,7-11$ $=4,-6,-4$ $=-2,3,2$ Now, we have one point $(-3,4,11)=\left(x_{1}, y_{1}, z_{1}\right)$ and direction ratios $(a, b, c)=-2,3,2$ $\because$ Equation of line : $\begin{aligned} & \frac{x-x_{1}}{a}=\frac{y-y_{1}}{b}=\frac{z-z_{1}}{c} \\ \Rightarrow \quad \frac{x+3}{-2} &=\frac{y-4}{3}=\frac{z-11}{2} \end{aligned}$

Hence, the correct answer is option: 'B'.

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