Question

The sine of the angle between the straight line \(\frac{x-2}{3}=\frac{y-3}{4}=\frac{z-4}{5}\) and the plane \(2 x-2 y+z=5\) is
(A) \(\frac{2 \sqrt{3}}{5}\)
(B) \(\frac{\sqrt{2}}{10}\)
(C) \(\frac{4}{5 \sqrt{2}}\)
(D) \(\frac{\sqrt{5}}{6}\)

Answer 1

Ans: (B)
Hint : Let the angle be \(\theta\). Then, \(\cos \left(90^{\circ}-\theta\right)=\frac{(3 \hat{i}+4 \hat{j}+5 \hat{k}) \cdot(2 \hat{i}-2 \hat{j}+\hat{k})}{|3 \hat{i}+4 \hat{j}+5 \hat{k}| \times|2 \hat{i}-2 \hat{j}+\hat{k}|} \Rightarrow \sin \theta=\frac{3}{\sqrt{50} \sqrt{9}}=\frac{\sqrt{2}}{10}\)

Answer 2

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Answer 3

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