How to Calculate the Angle Between a Vector and the Z-Axis?

[B-80]

[SOLVED] Finding the angle in a vector

hey these are normally easy, but I keep getting this wrong
Here are three displacements, each in meters: d1 = 5.0 i + 5.0 j -6.0 k, d2 = -1.0 i -1.0 j + 3.0 k, and d3 = 4.0 i + 3.0 j + 2.0 k.

(a) What is r = d1 - d2 + d3?
Got it right, 10,9,-7
(b) What is the angle between r and the positive z axis?
I am getting 127.87 degrees, but its wrong

I am taking the vector r's j and k, or y and z axes. then I am just doing sqrt(9^2 + -7^2) and then cos-1(-7/11.4(which is the mag)) can anyone help this is due in like 35 mins

 

[Mindscrape]

Are you using the dot product, or trig? Regardless, your magnitude for r is wrong, it should be sqrt(9^2 + 7^2 + 10^2). So the z leg is -7, which you got, and the magnitude gives the new magnitude. The angle would just he inverse cosine of that proportion.

 

[B-80]

if I put the mag at 15.17, it would mess it up right, because the vectors r axis doesn't have anything to do with z right, its up 9 and out -7 if you look at it straight on

are you saying its 117.49?

 

[bob1182006]

when finding the magnitude of a vector you can't just ignore one of the components.

0i+9j-7k =/= 10i+9j-7k

so the magnitude of the just 9j-7k is not equal to the magnitude of 10i+9j-7k

 

[Mindscrape]

Hmm, I'm not really sure what you mean by the r axis. Take three pencils and put them on the edge of table, each one representing the respective axis, and then point a stick out and down to represent your r vector. It wants the angle between the stick and the z axis directly, so ignore the x and the y pencils, and figure out the angle between the stick and the z pencil.

What you are proposing is to cut up some of the stick, and move it.