A line makes angles of 45° and 60° with the positive axis of X and Y respectively. The angle made by the same line with the positive axis of Z, is:

Question

A line makes angles of $45 °$ and $60 °$ with the positive axis of X and Y respectively. The angle made by the same line with the positive axis of Z, is:

Smart Achievers · Accepted Answer

(4)

Ans. 60° or 120°

Explanation:

Given $α = 45 °, β = 60 °, γ = ?$

$∵$ $\cos^{2} α + \cos^{2} β + \cos^{2} γ = 1$

$∴$ $\cos^{2} γ = 1 - \frac{1}{2} - \frac{1}{4} = \frac{1}{4}$

$\Rightarrow$ $γ = 60 ° or 120 °$

Solution

Q.
A line makes angles of $45 °$ and $60 °$ with the positive axis of X and Y respectively. The angle made by the same line with the positive axis of Z, is:

1 30° or 60°

2 60° or 90°

3 90° or 120°

4 60° or 120°

Ans.
(4)

Ans. 60° or 120°

Explanation:

Given $α = 45 °, β = 60 °, γ = ?$

$∵$ $\cos^{2} α + \cos^{2} β + \cos^{2} γ = 1$

$∴$ $\cos^{2} γ = 1 - \frac{1}{2} - \frac{1}{4} = \frac{1}{4}$

$\Rightarrow$ $γ = 60 ° or 120 °$

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