First slide

Direction ratios and direction cosines

Question

If a line OP makes angles of 45^o and 60^o with the positive axes of X and Y respectively.
The angle made by OP with the positive axis of Z is

Moderate

A

30^o or 60^o
B

60^o or 90^o
C

90^o or 120^o
D

60^o or 120^o

Solution

Given $α = 45^{\circ}, β = 60^{\circ}$
Now, $\cos^{2} α + \cos^{2} β + \cos^{2} γ = 1$
$\begin{array}{l} ∴ \cos^{2} γ = 1 - \frac{1}{2} - \frac{1}{4} = \frac{1}{4} \\ \Rightarrow γ = 60^{\circ} or 120^{\circ} \end{array}$

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