The projections of a vector on the three coordinate axis are $6,-3,2$ respectively. The direction cosines of…

The projections of a vector on the three coordinate axis are $6,-3,2$ respectively. The direction cosines of the vector are
  1. $6,-3,2$
  2. $\frac{6}{5},-\frac{3}{5}, \frac{2}{5}$
  3. $\frac{6}{7},-\frac{3}{7}, \frac{2}{7}$
  4. $-\frac{6}{7},-\frac{3}{7}, \frac{2}{7}$

Solution

Projection of a vector on coordinate axis are $x_2-x_1, y_2-y_1, z_2-z_1$ $ \begin{aligned} & x_2-x_1=6, y_2-y_1=-3, z_2-z_1=2 \\ & \sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2+\left(z_2-z_1\right)^2}=\sqrt{36+9+4}=7 \end{aligned} $ The D.C's of the vector are $\frac{6}{7},-\frac{3}{7}, \frac{2}{7}$

Asked in: JEE Main 2009

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