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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