First slide

Direction ratios and direction cosines

Question

If $α, β, γ$ are the angles which a line makes with the positive direction of coordinate axes, then the value of $\cos^{2} α - \sin^{2} β + \cos^{2} γ =$

Very Easy

A

0
B

1
C

2
D

3

Solution

If $α, β, γ,$ are the angles made by a line ‘L’ with the coordinate axes in the positive direction then $\cos^{2} α + \cos^{2} β + \cos^{2} γ = 1$
It implies that $\cos^{2} α + 1 - \sin^{2} β + \cos^{2} γ = 1 \Rightarrow \cos^{2} α - \sin^{2} β + \cos^{2} γ = 0$

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