Q73 / 160 · TS EAMCET 2022 (19 Jul Shift 2) · Mathematics

If the angle between the planes $\bar{r} \cdot(11 \hat{i}-2 \hat{j}+\alpha \hat{k})=7$ and $\bar{r} \cdot(2 \hat{i}+4 \hat{j}-2 \hat{k})=5$ is $\frac{\pi}{2}$, then $\alpha=$

  • A
    2
  • B
    3
  • C
    5
  • Correct answer
    D
    7

Solution

Given planes are $\bar{r} \cdot(11 \hat{i}-2 \hat{j}-\alpha \hat{k})=7$ and $\overline{\mathrm{r}} \cdot(2 \hat{\mathrm{i}}+4 \hat{\mathrm{j}}-2 \hat{\mathrm{k}})=5$ $\Rightarrow \mathrm{n}_1 \cdot \mathrm{n}_2=0 \Rightarrow 22-8-2 \alpha=0$ or $\alpha=7$

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

Relevant Questions