Question

A vector is 10 units long and points at 30° with respect to the x-axis. How many units does it point in the x direction?

Answer 1

|A| = magnitude of the vector
`\underset{A}{\rightarrow}`= 10 units

θ = angle of the vector
`\underset{A}{\rightarrow}` relative to positive x-axis = 30 degree

A' = component of vector
`\underset{A}{\rightarrow}` parallel to x-axis

Since the angle is made with the x-axis, hence the x-component of the vector
`\underset{A}{\rightarrow}` is given as

A' = |A| Cosθ

A' = (10) Cos30

A' = (10) (0.866)

A' = 8.66 units