Basic physics question - alpha particle moving through B-field

[Genericcoder]

An alpha particle is moving in the positive x direction with a speed of 0.0050c = 1.50 * 10^6. When the particle is at the orgin, find the magnetic field at a) P3: x = 1.0,y = 1.0,z = 1.0


The book answer is r3 = sqrt(3) = 1.73 and vecto r3 from q to p3 and vector v form a plane that makes an angle of 45 with the y and z axes. The angle Tehta between v and r3 is 54.7.


but I can't see how he got 54.7 like wouldn't it become arctan(1/sqrt(3)) I am good in 3d angles I didn't take it before.

 

[haruspex]

but I can't see how he got 54.7 like wouldn't it become arctan(1/sqrt(3)) .

No, it's not arctan(1/sqrt(3)). Draw the triangle with sides r3, v and v-r3. sqrt(3) is the hypotenuse.