Determine the angle between c= <5, -4> and d= <12, 7>. Please use right triangles!?

1 Answer
Somebody N.
Nov 10, 2017

#68.92^o# ( 2 .d.p.)

Explanation:

To find the angle between these two vectors we use the Dot Product. This gives the angle between them where they are moving in the same relative direction.

#C= ((5),(-4))#

#D=((12),(7))#

#||C||= sqrt((5)^2+(-4)^2)=sqrt(41)#

#||D||= sqrt((12)^2+(7)^2)=sqrt(193)#

#C*D = ((5),(-4))((12),(7))|C|*|D| cos(theta) #

#C*D=(60-28)=32#

#:.#

#32=sqrt(41)*sqrt(193)*cos(theta)#

#cos(theta)=32/(sqrt(41)*sqrt(193))=32/sqrt(7913)#

#theta= cos^-1cos(theta)=cos^-1(32/sqrt(7913))=68.92^o# ( 2 .d.p.)

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