Question

In Exercises 20-23, find the dot product of the given pairs of vectors and the angle between the two vectors.

Short answer

The dot product is 38 and the angle is${\cos }^{-1}\left(\frac{38}{\sqrt{2170}}\right)$.

Step-by-step solution

Step 1. Given information.

The given pairs of vectors are:

Step 2. Find the dot product.

The dot product is:$\mathit{u}\mathbf{·}\mathit{v}=u_1{v}_1+u_2{v}_2+u_3{v}_3$

Therefore, the dot product of the given two vectors is 38.

Step 3. Find the angle between the two vectors.

The formula for the angle between the two vectors is:

Then,

$$\begin{gathered} \cos \theta =\frac{\mathit{u}\mathbf{·}\mathit{v}}{||\mathit{u}||||\mathit{v}||} \\ \cos \theta =\frac{38}{\sqrt{35}\sqrt{62}} \\ \theta ={\cos }^{-1}\left(\frac{38}{\sqrt{2170}}\right) \end{gathered}$$

Therefore, the angle is${\cos }^{-1}\left(\frac{38}{\sqrt{2170}}\right)$.