The magnitudes of the vectors in this diagram are
vx/y = 17.94 meters/second and
vy/z = 3.46 meters/second. find vx/z.

14.48 m/s

Explanation:

According to the addition law of vectors, if there are two vectors A and B acting at an angle Ф, then the resultant is given by

Here the angle between Vx/y and Vy/z is 180 degree, so the resultant is given by

R = Vx/y - Vy/z

R = 17.94 - 3.46

R = 14.48 m/s

see the picture for the vector

the magnitude of the vector by pythagorean theorem

r = √( (-10)^2 + (3)^2 ) = √109

magnitude = √109 units

the direction angle between vector and x-axis is

tan^(-1)(3/10) = 16.699

so the direction is approximately 16.7 degrees north of west