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NDA 2022
Exam
NDA
Year
2022
Subject
Mathematics
Chapter
Three Dimensional Geometry

NDA 2022 · Mathematics · Three Dimensional Geometry

Let the plane (2 x)/(k)+(2 y)/(3)+(z)/(3)=2 pass through the point...

Let the plane 2xk+2y3+z3=2\frac{2 x}{k}+\frac{2 y}{3}+\frac{z}{3}=2 pass through the point (2,3,−6)(2,3,-6). If p,qp, q and rr are the intercepts made by the plane on the coordinate axes respectively, then what is (p+q+r)(p+q+r) equal to?

Options

  1. A10
  2. B11
  3. C12
  4. D13

Correct answer

B. 11

Step-by-step solution

3x+2y+z=6x2+y3+z6=1\begin{aligned} & 3 x+2 y+z=6 \\ & \frac{x}{2}+\frac{y}{3}+\frac{z}{6}=1\end{aligned}\thereforeInterceptonaxesareIntercept on axes are2,3,6respectivelyrespectively∴P=2,q=3 and r=6∴p+q+r=2+3+6=11\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}$
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