Find the angle θ between the vectors v and w

Question

v = (7,2,−10), w = (2,6,4)

Answer 1

v•w = 7(2) + 2(6) + (-10)(4) = 14 + 12 - 40 = -14

 

||v|| = √(7² + 2² + (-10)²) = √(49 + 4 + 100) = √153 = 3√17

 

||w|| = √(2² + 6² + 4²) = √(4+36+16) = √56 = 2√14

 

||v||*||w|| = (3√17)*(2√14) = 6√238 

 

cos θ = v•w  / (||v||*||w||) = -14 / (6√238) = -.15125

 

θ = cos^-1 (-.15125) = 98.7 degrees