Question

A vector has an x-component equal to 0.15 and a y-component is equal to 1.22 calculate the vectors direction relative to the positive x-axis

Answer 1

The vector direction is 83.0° relative to the positive x-axis

Explanation:

* Lets explain how to find the direction of a vector

- A vector is a quantity which has both magnitude and direction

- The vector has two components x-component and y-component

- The x-component = v cos Ф , and the y-component = v sin Ф,

where Ф is the angle between the vector and the positive part

of the x-axis

- The magnitude of the vector =
`\sqrt{x^(2)+y^(2)}`

- The direction of the vector =
`tan^(-1)((y)/(x))`

* Lets solve the problem

∵ x-component of the vector = 0.15

∵ y-component of the vector = 1.22

- Both x-component and y-component are positive

∴ Ф will be between 0° and 90°

∵ The direction of the vector =
`tan^(-1)((y)/(x))`

∴ The direction of the vector =
`tan^(-1)((1.22)/(0.15))`

∴ The direction of the vector = 83.0°

* The vector direction is 83.0° relative to the positive x-axis