Direction Cosines

Q. If a line makes an angle of 90°, 60°, 30° with the positive direction of
x, y, z-axis, respectively, then find its direction cosines.

1. (0, 2, 1)
2. $\left(0,\frac{1}{2},\frac{\sqrt{3}}{2}\right)$
3. $\left(\frac{1}{2},0,\frac{\sqrt{3}}{2}\right)$
4. 
   $\left(0,\frac{1}{2},\frac{3}{2}\right)$

Q. If a line makes an angle of 90°, 60°, 30° with the positive direction of
x, y, z-axis, respectively, then find its direction cosines.

1. (0, 2, 1)
2. $\left(0,\frac{1}{2},\frac{\sqrt{3}}{2}\right)$
3. $\left(\frac{1}{2},0,\frac{\sqrt{3}}{2}\right)$
4. 
   $\left(0,\frac{1}{2},\frac{3}{2}\right)$

Q. The projection of any line on co-ordinate axes be respectively 3, 4, 5 then its length is

1. 12
2. 50
3. $5\sqrt{2}$
4. 25

Q. A straight line, makes an angle of ${60}^{\circ }$ with each of y and z-axis, then the inclination of the line with x-axis is

1. ${60}^{\circ }$
2. ${30}^{\circ }$
3. ${45}^{\circ }$
4. ${75}^{\circ }$

Q. A straight line, makes an angle of ${60}^{\circ }$ with each of y and z-axis, then the inclination of the line with x-axis is

1. ${60}^{\circ }$
2. ${30}^{\circ }$
3. ${45}^{\circ }$
4. ${75}^{\circ }$

Q. If a line makes the angle $\alpha ,\beta ,\gamma$ with three dimensional co-ordinate axes respectively, then $cos2\alpha +cos2\beta +cos2\gamma$

1. -2
2. -1
3. 1
4. 2

Q. In 3D space, a line can make $60°$ angle from each axis

1. False
2. True