# If A = <2 ,1 ,8 >, B = <5 ,2 ,3 > and C=A-B, what is the angle between A and C?

Jun 10, 2018

$\theta \approx {47.82}^{\circ}$

#### Explanation:

$C = A - B = \left(2 , 1 , 8\right) - \left(5 , 2 , 3\right) = \left(- 3 , - 1 , 5\right)$

$A \cdot C = | A | | C | \cos \theta$

cos theta = {A cdot C}/{|A||C|} = {2(-3)+1(-1)+8(5)}/{sqrt{(2^2+1^2+8^2)(3^2+1^2+5^2)} }= 11 sqrt(3/805)

$\theta \approx {47.82}^{\circ}$