Find the angle between the given vectors to the nearest tenth of a degree. u = <6, -1>, v = <7, -4>

Answer 1

a =<6,-1>  b =<7,-4>

Use the formula

cos θ =(a ⋅ b)/(|a||b|)

if a =<x1,y1>   b= <x2,y2>

a ⋅ b =x1x2+y1y2

a ⋅ b =(6)(7)+(-1)(-4)

       =42+4

       =46

Calculate the magnitudes:

|a| =√((6)^2+(-1)^2)

    =√(36+1)

    =√37

|b| =√((7)^2+(-4)^2)

    =√(49+16)

    =√65

 

cos θ =(a ⋅ b)/(|a||b|)

          =46/(√37)(√65)

          =46/√2405

          =0.938

θ =cos^-1(0.938)

   =20.28