JEE Main · 2009 · 12 Apr 2009 · Offline · Three Dimensional Geometry

The projections of a vector on the three coordinate axis are

6, - 3, 2

respectively. The direction cosines of the vector are

(A) $6, - 3, 2$
(B) $\frac{6}{5}, - \frac{3}{5}, \frac{2}{5}$
(C) $\frac{6}{7}, - \frac{3}{7}, \frac{2}{7}$ ✓ Correct
(D) $- \frac{6}{7}, - \frac{3}{7}, \frac{2}{7}$

Answer: (C)

Solution

The projections of the vector on the axes are just its components,

6, - 3, 2

, so its magnitude is

6^{2} + (- 3)^{2} + 2^{2} = 49 = 7

. Dividing each component by this length gives the direction cosines

\frac{6}{7}, - \frac{3}{7}, \frac{2}{7}

JEE Main · 2009 · 12 Apr 2009 · Offline · Single correct option

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