Q209 / 270 · NDA 2012 (Phase 2) · Mathematics

What are the direction ratios of the line of intersection of the planes $x=3 z+4$ and $y=2 z-3$ ?

  • A
    $\langle 1,2,3\rangle$
  • B
    $\langle 2,1,3\rangle$
  • Correct answer
    C
    $\langle 3,2,1\rangle$
  • D
    $\langle 1,3,2\rangle$

Solution

$\begin{array}{ll} & x=3 z+4 \\ \text { and } & y=2 z-3\end{array}$ $\Rightarrow \quad \frac{x-4}{3}=z$ and $\quad \frac{y+3}{2}=z$ $\Rightarrow \quad \frac{x-4}{3}=\frac{y+3}{2}=\frac{z}{1}$ $\therefore$ Direction ratios are proportional to $ \lt 3,2,1 \gt $.

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

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