What is the angle in radians between the vectors

Question

What is the angle in radians between the vectors?

 

a= (-2, -2, 3) and
b = (-4, 0, 7)

 

angle?

Answer 1

Hi again, Burak

 

The formula for the cosine of the angle between two vectors is 

 

cos(Θ)=[a•b]/[|a| |b|]

 

so the cos(Θ) = [(-2)(-4) + (-2)(0) + (3)(7)] / [sqrt(4 + 4 + 9) * sqrt(16 + 0 + 49)

 

cosΘ=29/[sqrt(17)sqrt(65)

 

cosΘ=29/sqrt(1105) ≈ 0.8724

 

Now use the inverse cosine function on  your calculator and find

 

cos^-1(0.8724) = 0.510705 radians