AP EAMCET · Maths · Three Dimensional Geometry
If a line makes angles \(90^{\circ}, 135^{\circ}\) and \(45^{\circ}\) with the positive \(X, Y\) and \(Z\) axis respectively, then its direction cosines are
- A \(\left(0, \frac{1}{2}, \frac{1}{\sqrt{2}}\right)\)
- B \(\left(0, \frac{-1}{\sqrt{2}}, \frac{1}{\sqrt{2}}\right)\)
- C \(\left(1, \frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}}\right)\)
- D \(\left(1, \frac{-1}{\sqrt{2}}, \frac{1}{\sqrt{2}}\right)\)
Answer & Solution
Correct Answer
(B) \(\left(0, \frac{-1}{\sqrt{2}}, \frac{1}{\sqrt{2}}\right)\)
Step-by-step Solution
Detailed explanation
Given, a line makes \(90^{\circ}, 135^{\circ}\) and \(45^{\circ}\) with the positive \(x, y\) and \(z\) axes respectively. Hence, it's direction cosines are \( \) \(=\left(0, \frac{-1}{\sqrt{2}}, \frac{1}{\sqrt{2}}\right)\)
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