Q99 / 160 · TS EAMCET 2024 (09 May Shift 2) · Mathematics

$(3,0,2)$ and $(0,2, k)$ are the direction ratios of two lines and $\theta$ is the angle between them. If $|\cos \theta|=\frac{6}{13}$, then $k=$

  • A
    $\pm 2$
  • Correct answer
    B
    $\pm 3$
  • C
    $\pm 5$
  • D
    $\pm 7$

Solution

$(3,0,2)$ and $(0,2, k)$ $\begin{aligned} & |\cos \theta|=\frac{0+0+2 k}{\sqrt{9+4} \sqrt{4+k^2}} \Rightarrow \frac{6}{13}=\frac{2 k}{\sqrt{13} \sqrt{4+k^2}} \\ & \Rightarrow \frac{3}{\sqrt{13}}=\frac{k^2}{\sqrt{4+k^2}} \Rightarrow \frac{9}{13}=\frac{k^2}{4+k^2} \Rightarrow k= \pm 3 .\end{aligned}$

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

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