Vector a has a magnitude of 50 units and points in the positive x direction. a second vector, b , has a magnitude of 120 units and points at an angle of 70 degrees below the x axis.

part a

which vector has the greater x component.

part b

which vector has the greater y component?

A) Vector A

The x-component of a vector can be found by using the formula

where

v is the magnitude of the vector

is the angle between the x-axis and the direction of the vector

- Vector A has a magnitude of 50 units along the positive x-direction, so . So its x-component is

- Vector B has a magnitude of 120 units and the direction is (negative since it is below the x-axis), so the x-component is

So, vector A has the greater x component.

B) Vector B

Instead, the y-component of a vector can be found by using the formula

Here we have

- Vector B has a magnitude of 50 units along the positive x-direction, so . So its y-component is

- Vector B has a magnitude of 120 units and the direction is , so the y-component is

where the negative sign means the direction is along negative y:

So, vector B has the greater y component.