UPSC NDA Math Model Paper 7

Given: A vector is equally inclined to the x-axis, y-axis and z-axis respectively.
Therefore, α = β = γ
As we know that, cos‌2 α + cos‌2 β + cos‌2 γ = 1
⇒ cos‌2 α + cos‌2 α + cos‌2 α = 1
⇒ 3 cos‌2 α = 1
⇒ cos‌2 α = 1/3
∴ cos α =±(1∕√3)
Therefore, cos α = cos β = cos γ =±(1∕√3)
So, l = m = n =±(1∕√3)
Now, Direction cosine of the vector is <

1

√3

,

1

√3

,

1

√3

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