Determine the angle relative to the #x# axis given by the vector #-3hati - 5hatj#?

1 Answer
Truong-Son N.
Dec 1, 2017

Here's another way to write this.

#-3hati - 5hatj#

#= -(3hati + 5hatj)#

#= - << 3, 5 >>#

#= << -3, -5 >>#

This vector points in the #x = -3#, #y = -5# direction. I don't know which angle you want, but counterclockwise relative to the positive #x# axis is a common convention.

The angle relative to the positive #x# axis is #180^@# counterclockwise plus the angle from the #-x# axis, which means:

#color(blue)(theta) = 180^@ + [arctan(5/3)] cdot (180^@/pi) ~~ color(blue)(239^@)#

where #arctanx# is the inverse function of #tanx#.

Or about #59^@# counterclockwise from the #-x# axis.

Related questions
Impact of this question
68 views around the world
You can reuse this answer
Creative Commons License