Question

Find the angles that vector →D=(2.0ˆi−4.0ˆj+ˆk)m makes with the x-, y-, and z- axes.

a) x-axis: 63.4°, y-axis: 116.6°, z-axis: 90°
b) x-axis: 63.4°, y-axis: 90°, z-axis: 63.4°
c) x-axis: 90°, y-axis: 63.4°, z-axis: 116.6°
d) x-axis: 116.6°, y-axis: 63.4°, z-axis: 90°

Answer 1

a) x-axis: 63.4°, y-axis: 116.6°, z-axis: 90°

The angles that vector →D makes with the x-, y-, and z-axes are calculated using trigonometric functions and correspond to option (a).

Step-by-step explanation:

To find the angles vector →D makes with the axes, you can use trigonometric functions. The angle θ between a vector and a coordinate axis can be calculated using the formula:
`\( \theta = \arccos\left(\frac{A \cdot \hat{i}}{|\vec{A}|}\right) \)` for the x-axis,
`\( \theta = \arccos\left(\frac{A \cdot \hat{j}}{|\vec{A}|}\right) \)` for the y-axis, and
`\( \theta = \arccos\left(\frac{A \cdot \hat{k}}{|\vec{A}|}\right) \)` for the z-axis.

For vector →D, the angles are approximately x-axis: 63.4°, y-axis: 116.6°, z-axis: 90°, which corresponds to option (a).