# If A = <4 ,-9 ,2 >, B = <1 ,1 ,-4 > and C=A-B, what is the angle between A and C?

Apr 13, 2017

The angle between $\vec{A} \mathmr{and} \vec{C}$ is ${19.60}^{0}$

#### Explanation:

Let $\vec{A} = < 4 , - 9 , 2 > , \vec{B} = < 1 , 1 , - 4 > , \vec{C} = \vec{A} - \vec{B} = < 3 , - 10 , 6 >$ ;

Let $\theta$ be the angle between $\vec{A} \mathmr{and} \vec{C}$ ; then we know $\cos \theta = \frac{\vec{A} \cdot \vec{C}}{| | \vec{A} | | \cdot | | \vec{C} | |}$

=((4*3)+(-9*-10)+(2*6))/(sqrt(4^2+(-9)^2+2^2)* (sqrt(3^2+(-10)^2+6^2)) $= \frac{114}{\sqrt{101} \cdot \sqrt{145}} = 0.94202 \therefore \theta = {\cos}^{-} 1 \left(0.94202\right) \approx {19.60}^{0}$[Ans]