Q. 95.0( 1 Vote )

# <span lang="EN-US

Given, the line makes the angles α, β and γ respectively with x-axis, y-axis and z-axis.

As per the relation between direction cosines of a line, l2 + m2+n2 = 1 where l,m,n are the direction cosines of a line from x-axis, y-axis and z-axis respectively.

So, we can say that,

cos2α + cos2β + cos2γ = 1 ------ (1)

Now, we should find the value for

cos2α + cos2β + cos2γ

cos2α can be written as 2cos2α -1,

cos2α + cos2β + cos2γ = (2cos2α -1) + (2cos2β -1) + (2cos2γ -1)

= 2 (cos2α+ cos2β + cos2γ) – 3

= 2(1) – 3

[From Equation (1)]

= -1

Therefore,

cos2α + cos2β + cos2γ = -1

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