Determine the angle between the following vector and the zax

Determine the angle between the following vector and the z-axis, indicate its value in degrees. Create and use any vector in the z-direction. Draw the vectors and see if your answer makes sense!

q1=[6 -4 6]

Solution

Unit vector along z axis is: k

Given vector is:

q1=6i-4j+6k

SO, q1.k=6=|q1|cos(x)

x is angle between q1 and z axis

|q1|=sqrt{6^2+4^2+6^2}=sqrt{88}=2sqrt{22}

HEnce, cos(x)=3/sqrt{22}~50.24 degrees