Question

Determine the angles made by the vector V = (-36)i + (29)j with the positive x- and y-axes (enter the smallest possible positive values). Write the unit vector n in the direction of V.

Answer 1

Step-by-step explanation:

`\overrightarrow{V}=-36\widehat{i}+29\widehat{j}`

Let the given vector makes an angle θ from positive X axis

`tan\theta =(vertical component)/(horizontal component)=\frac {29}{-36}`

tanθ = -0.8055

θ = -38.85° from + X axis, i.e. 321.15° from + X axis in counter clock wise direction

Angle made from + y axis = 321.15° - 90° = 231.15°

Magnitude of V =
`\sqrt{\left ( -36 \right )^(2)+\left ( 29 \right )^(2)=46.23`

The unit vector in the direction of V is given by

`\widehat{n}=\frac {\overrightarrow{V}}{V}`

`\widehat{n}=\frac{-36\widehat{i}+29\widehat{j}}{46.23}`