How can I find angle θ between two vectors?

There are two I'm stuck on

1) u = <3, 2>

v = <4, 0>

I definitely struggle with these types of problems so if there's any pointers for remembering formulas etc that'd be greatly appreciated :)

1 Answer
Kalit Gautam
Feb 22, 2018

#vecu.vecv = |vecu||vecv|cos θ#

This is the Formula for Dot product of two vectors; can also be used to find the angle between these vectors.

Explanation:

#:. cos θ = (vecu.vecv)/(|vecu||vecv|)#

#rArr θ = cos^(-1)[(vecu.vecv)/(|vecu||vecv|)]#

#rArr θ = cos^(-1){ (<3, 2>.<4, 0>)/((3^2+2^2)^(1/2).(4^2+0^2)^(1/2))}#

#rArr θ = cos^(-1){12/(4.(13)^(1/2))}#

#:.θ = cos^(-1){3/(13)^(1/2)}# #rArrθ = 0.588° #

NOTE = To remember the formula, write it again and again on your rough notebook and Yes do a lot of questions based on that formula. Practice and hardwork is the only key to success.............................................😊😊😊

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