If the adjacent sides of a rectangle are $\bar{a}=5 \bar{m}-3 \bar{n}, \bar{b}=-\bar{m}-2 \bar{n}$ and the…

If the adjacent sides of a rectangle are $\bar{a}=5 \bar{m}-3 \bar{n}, \bar{b}=-\bar{m}-2 \bar{n}$ and the adjacent sides of another rectangle are $\bar{c}=-4 \bar{m}-\bar{n}, \bar{d}=-\bar{m}+\bar{n}$, then the angle between the vectors $\bar{x}=\frac{\bar{a}+\bar{c}+\bar{d}}{3}$ and $\bar{y}=\frac{\bar{c}+\bar{d}}{5}$ is
  1. $\frac{\pi}{2}$
  2. $\operatorname{Cos}^{-1}\left(\frac{19}{5 \sqrt{43}}\right)$
  3. $\operatorname{Cos}^{-1}\left(\frac{19}{5 \sqrt{43}}\right)+\pi$
  4. $\operatorname{Sin}^{-1} \frac{19}{4 \sqrt{43}}$

Solution

No solution. Refer to answer key.

Asked in: AP EAMCET 2018 (24 Apr Shift 2)

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