# How do you use the definition of the scalar product, find the angles between the following pairs of vectors: A = -i - 2k and B = - 5i + 5j + 5k?

Nov 11, 2016

The angle is =105º

#### Explanation:

The dot product of $\vec{A}$ and $\vec{B}$
is given by vecA.vecB=∥vecA∥.∥vecB∥costheta
where $\theta$ is the angle between the 2 vectors.
Here, vecA=〈-1,0,-2〉 and vecB=〈-5,5,5〉

The dot product vecA.vecB=〈-1,0,-2〉.〈-5,5,5〉=5+0-10=-5

The modulus of vecA=∥〈-1,0,-2〉∥=sqrt(1+0+4)=sqrt5

The modulus of vecB=∥〈-5,5,5〉∥=sqrt(25+25+25)=sqrt75

cos theta=(vecA.vecB)/(∥vecA∥.∥vecB∥)=-5/(sqrt5*sqrt75)=-1/sqrt15=-0.258

theta=105º