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 13 and the angle is$4.439°$.

Step-by-step solution

Step 1. Given information.

The given pairs of vectors are:

Step 2. Find the dot product.

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

Therefore, the dot product of the given two vectorsis 13.

Step 3. Find the angle between the two vectors.

The formula for the angle $\theta$between the two vectors is:

$\cos \theta =\frac{\mathit{u}\mathbf{·}\mathit{v}}{||\mathit{u}||||\mathit{v}||}$

Then,

$$\begin{gathered} \cos \theta =\frac{\mathit{u}\mathbf{·}\mathit{v}}{||\mathit{u}||||\mathit{v}||} \\ =\frac{13}{\sqrt{5}\sqrt{34}} \\ =\frac{13}{\sqrt{170}} \\ \theta ={\cos }^{-1}\left(\frac{13}{\sqrt{170}}\right) \\ =4.439° \end{gathered}$$

Therefore, the angle is$4.439°$.