Find the magnitude and direction of vector R? ?

Question

The x vector component of a displacement vector R has a magnitude of 115 m and points along the negative x axis. The y vector component has a magnitude of 111 m and points along the negative y axis. Find (a) the magnitude and (b) direction of vector R . Specify the direction as a positive angle with respect to the negative x axis.

I am not sure how to start this problem? any help would be appreciated

Answer 1

Suppose the displacement vector R is acting on a particle on origin. The particle will be displaced to a point whose coordinates can be given by (-115,-111).

Now, the magnitude of displacement vector R is given by

|R| = sqrt[ (-115-0)² + (-111-0)²]

     = sqrt[ 25546]

     = 160m (approximately)

The direction can be found by,

Ø = tan^-1(111/115)

    = 44° (approximately)