Right hand rule, vector and angles

[SPhy]

Homework Statement

A particle with a unit charge enters a magnetic field B = i + j with velocity v = 17k . Find the magnitude and direction of the force on the particle.

The Attempt at a Solution

Had no issues finding the magnitude. However, when finding the direction of the force on the particle, the textbook says by the right hand rule the force is applied at an angle of 135 degrees with the positive x-axis in the xy-plane. I understand how to apply the right hand rule and show the general direction of the vector ( I sketched it), but how did they come up with 135?

Thank you

 

[Curious3141]

Homework Statement

A particle with a unit charge enters a magnetic field B = i + j with velocity v = 17k . Find the magnitude and direction of the force on the particle.

The Attempt at a Solution

Had no issues finding the magnitude. However, when finding the direction of the force on the particle, the textbook says by the right hand rule the force is applied at an angle of 135 degrees with the positive x-axis in the xy-plane. I understand how to apply the right hand rule and show the general direction of the vector ( I sketched it), but how did they come up with 135?

Thank you

Sketch the x-y-z axes (in a right-handed orientation so that the right-hand rule applies).

What's the angle that the magnetic field vector makes with the x-axis?

Remember that 135 = 90 + 45. Is that sufficient for you to figure it out?

 

[Dick]

The picture here might help as well. http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/magfor.html You could also just do the cross product. k x i=j and k x j=(-i).