The acute angle between the line \(\displaystyle\frac{x-2}{1}=\frac{y+1}{\sqrt{2}}=\frac{z-3}{1}\) and the y-axis is
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → \(\displaystyle\frac{\pi}{4}\)
The direction ratios of the line are \(1, \sqrt{2}, 1\), and the y-axis has direction ratios 0, 1, 0.
\(\sqrt{1^2+(\sqrt{2})^2+1^2} = \sqrt{4} = 2\)
The angle between two lines is given by
\( \displaystyle \cos\theta = \frac{|(1)(0)+(\sqrt{2})(1)+(1)(0)|}{2 \times 1} = \frac{\sqrt{2}}{2} = \frac{1}{\sqrt{2}} \)
\( \displaystyle \theta = \frac{\pi}{4} \)