Question

Evaluate the dot product of the three pairs of vectors in

Figure

Short answer

a).$\overrightarrow{A}·\overrightarrow{B}=-2.7$

b).role="math" localid="1648057299716" $\overrightarrow{C}·\overrightarrow{D}=-20$

c).$\overrightarrow{E}·\overrightarrow{F}=10$

Step-by-step solution

Step 1. Given Information

We have,

The dot product is the sum of the product of the component where this dot product is called the scalar product.

For two vector $A$and $B$and there is an angle $\alpha$between then the dot product these two vectors is given by

$$\begin{gathered} \overrightarrow{A}·\overrightarrow{B}=AB\cos \alpha \\ \overrightarrow{C}·\overrightarrow{D}=CD\cos \alpha \\ \overrightarrow{E}·\overrightarrow{F}=EF\cos \alpha \end{gathered}$$

Step 2. Part a). A and B are the magnitude α is the angle

We are given by $A=3$and $B=5$and the angle is$\alpha =110°$

So,

$$\begin{gathered} \overrightarrow{A}·\overrightarrow{B}=AB\cos \alpha \\ =\left(2\right)\left(4\right)\cos 110° \\ =-2.7 \end{gathered}$$

Step 3. Part b). C and D are the magnitude α is the angle

The magnitude of the vector by $C=4$and $D=5$and the angle is role="math" localid="1648059175573" $\alpha =180°$

So,

$$\begin{gathered} \overrightarrow{C}·\overrightarrow{D}=CD\cos \alpha \\ =\left(4\right)\left(5\right)\cos 180° \\ =-30 \end{gathered}$$

Step 4. Part c). E and F are the magnitude and α is angle

The magnitude of the vector by $E=4$and $F=3$and the angle is $\alpha =30°$

So,

$$\begin{gathered} \overrightarrow{E}·\overrightarrow{F}=EF\cos \alpha \\ =\left(4\right)\left(3\right)\cos 30° \\ =10 \end{gathered}$$