
John M. answered 02/12/20
Math Teacher/Tutor/Engineer - Your Home, Library, MainStreet or Online
Find the angle between -5i+12j and 3i+2j.
The simple geometric way is:
-5i +12j makes an angle of arctan(-5/12) = 22.6° from vertical
3i +2j makes and angle of 56.31° from vertical
Adding these two angles together yields the angle between the two vectors of 78.9°
The vector way is:
cos-1θ=(u,v)∥u∥∥v∥ where u = -5i+12j and v = 3i+2j.
u·v is the dot product = -5 x 3 + 12 x 2 = -15 + 24 = 9
Absolute values are :√(52 + 122 ) = 13 and √( 32 + 22) = √13
Then cos-1θ = 9/(13√13) = 78.9°