COMEDK · Maths · 34. Three Dimensional Geometry
A line makes the same angle \(\theta\) with each of the \(x\) and \(z\)-axes. If the angle \(\beta\), which it makes with the \(y\)-axis is such that \(\sin ^2 \beta=3 \sin ^2 \theta\), then \(\cos ^2 \theta\) equals
- A \(\dfrac{2}{3}\)
- B \(\dfrac{2}{5}\)
- C \(\dfrac{1}{5}\)
- D \(\dfrac{3}{5}\)
Answer & Solution
Correct Answer
(D) \(\dfrac{3}{5}\)
Step-by-step Solution
Detailed explanation
Let the direction cosines of the line be \(l, m, n\). Since the line makes the same angle \(\theta\) with the \(x\) and \(z\)-axes, we have \(l = \cos \theta\) and \(n = \cos \theta\). Let \(\beta\) be the angle the line makes with the \(y\)-axis, so \(m = \cos \beta\). The sum…
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