If l, m, n are the direction cosines of a position vector \(\vec{a}\), then which of the following is true?(a) l^2+m^2-n^2=0(b) lmn=1(c) l^2+m^2+n^2=1(d) l^2 m^2+n^2=1This question was posed to me during an online interview.Enquiry is from Vector Algebra Basics in portion Vector Algebra of Mathematics – Class 12

If l, m, n are the direction cosines of a position vector \(\vec{a}\),

1.	If l, m, n are the direction cosines of a position vector \(\vec{a}\), then which of the following is true?(a) l^2+m^2-n^2=0(b) lmn=1(c) l^2+m^2+n^2=1(d) l^2 m^2+n^2=1This question was posed to me during an online interview.Enquiry is from Vector Algebra Basics in portion Vector Algebra of Mathematics – Class 12
Answer» Correct choice is (c) l^2+m^2+n^2=1 Explanation: Consider \(\vec{a}\) is the position VECTOR of a POINT M(x,y,z) andα, β, γ are the angles, MADE by the vector \(\vec{a}\) with the positive directions of x, y and z respectively. The cosines of the angles, cos⁡α, cos⁡β, cos⁡γ are the DIRECTION cosines of the vector \(\vec{a}\) denoted by l, m, n, then cos^2⁡α+cos^2⁡β+cos^2⁡γ=1 i.e.l^2+m^2+n^2=1.

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