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Question

Mathematics Question on Three Dimensional Geometry

The projections of a vector on the three coordinate axis are 6,−3,26, - 3, 2 respectively. The direction cosines of the vector are

A

6,−3,26, - 3, 2

B

65,−35,25\frac{6}{5}, -\frac{3}{5}, \frac{2}{5}

C

67,−37,27\frac{6}{7}, -\frac{3}{7}, \frac{2}{7}

D

−67,−37,27-\frac{6}{7}, -\frac{3}{7}, \frac{2}{7}

Answer

67,−37,27\frac{6}{7}, -\frac{3}{7}, \frac{2}{7}

Explanation

Solution

Projection of a vector on coordinate axis are x2−x1,y2−y1,z2−z1x_2-x_1, y_2-y_1, z_2-z_1 x2−x1=6,y2−y1=−3,z2−z1=2x_2 - x_1 = 6, y_2 - y_1 = -3, z_2 - z_1 = 2 (x2−x1)2+(y2−y1)2+(z2−z1)2=36+9+4=7\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 The D.C?? of the vector are 67,−37,27\frac{6}{7}, -\frac{3}{7}, \frac{2}{7}