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Question: Answered & Verified by Expert
The projections of a vector on the three coordinate axis are $6,-3,2$ respectively. The direction cosines of the vector are
MathematicsThree Dimensional GeometryJEE MainJEE Main 2009
Options:
  • A
    $6,-3,2$
  • B
    $\frac{6}{5},-\frac{3}{5}, \frac{2}{5}$
  • C
    $\frac{6}{7},-\frac{3}{7}, \frac{2}{7}$
  • D
    $-\frac{6}{7},-\frac{3}{7}, \frac{2}{7}$
Solution:
1983 Upvotes Verified Answer
The correct answer is:
$\frac{6}{7},-\frac{3}{7}, \frac{2}{7}$
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 $\frac{6}{7},-\frac{3}{7}, \frac{2}{7}$

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