Question

The angle between the vectors a=2i+3j and b=6i-4j is

Answer 1

Answer:

We're asked to find the angle between two vectors, given their unit vector notations.

To do this, we can use the equation

→A⋅→B=ABcosθ

rearranging to solve for angle, θ:

cosθ=→A⋅→BAB

θ=arccos⎛⎝→A⋅→BAB⎞⎠

where

   →A⋅→B is the dot product of the two vectors, which is

   →A⋅→B=AxBx+AyBy+AzBz

   =(2)(1)+(3)(2)+(1)(−4)=4

   A and B are the magnitudes of vectors →A and →B, which are

   A=√22+32+12=√14

   B=√12+22+(−4)2=√21

Therefore, we have

θ=arccos(4√14√21)=arccos(47√6)=76.5o