MHT CET · Maths · Three Dimensional Geometry
The direction co-sines of the line which bisects the angle between positive direction of \(Y\) and \(Z\) axes are
- A \(\frac{1}{\sqrt{2}}, 0, \frac{1}{\sqrt{2}}\)
- B \(\frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}}, 0\)
- C \(0, \frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}}\)
- D \(\frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}}\)
Answer & Solution
Correct Answer
(C) \(0, \frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}}\)
Step-by-step Solution
Detailed explanation
(C)
Vector parallel to bisector of angle between positive \(\mathrm{Y}\) and \(\mathrm{Z}\) direction. \(=\hat{\mathrm{j}}+\hat{\mathrm{k}}\) and its magnitude is \(\sqrt{1+1}=\sqrt{2}\)
\(\therefore\) Direction cosines \(=\left(0, \frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}}\right)\)
Vector parallel to bisector of angle between positive \(\mathrm{Y}\) and \(\mathrm{Z}\) direction. \(=\hat{\mathrm{j}}+\hat{\mathrm{k}}\) and its magnitude is \(\sqrt{1+1}=\sqrt{2}\)
\(\therefore\) Direction cosines \(=\left(0, \frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}}\right)\)
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