Q245 / 270 · NDA 2022 (Phase 1) · Mathematics

Let the plane $\frac{2 x}{k}+\frac{2 y}{3}+\frac{z}{3}=2$ pass through the point $(2,3,-6)$. If $p, q$ and $r$ are the intercepts made by the plane on the coordinate axes respectively, then what is $(p+q+r)$ equal to?

  • A
    10
  • Correct answer
    B
    11
  • C
    12
  • D
    13

Solution

$\begin{aligned} & 3 x+2 y+z=6 \\ & \frac{x}{2}+\frac{y}{3}+\frac{z}{6}=1\end{aligned}$ $\therefore$ Intercept on axes are $2,3,6$ respectively $\begin{aligned} & \therefore \mathrm{P}=2, \mathrm{q}=3 \text { and } \mathrm{r}=6 \\ & \therefore \mathrm{p}+\mathrm{q}+\mathrm{r}=2+3+6=11\end{aligned}$

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

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