Question

Find the dot product of bold v equals negative 7 bold i plus 4 bold j and bold w equals negative 6 bold i plus 5 bold j.
(1 point)
Responses

negative 62
Image with alt text: negative 62

negative 22
Image with alt text: negative 22

22
22

62

Answer 1

To find the dot product of the vectors **v** and **w**, we can use the formula for the dot product:

\[
\mathbf{v} \cdot \mathbf{w} = v_x w_x + v_y w_y
\]

where \(\mathbf{v} = -7 \mathbf{i} + 4 \mathbf{j}\) and \(\mathbf{w} = -6 \mathbf{i} + 5 \mathbf{j}\).

Here, we identify:
- \(v_x = -7\), \(v_y = 4\)
- \(w_x = -6\), \(w_y = 5\)

Now we can substitute these values into the dot product formula:

\[
\mathbf{v} \cdot \mathbf{w} = (-7)(-6) + (4)(5)
\]

Calculating each term:

\[
(-7)(-6) = 42
\]
\[
(4)(5) = 20
\]

Now, adding these results together:

\[
\mathbf{v} \cdot \mathbf{w} = 42 + 20 = 62
\]

Therefore, the dot product of **v** and **w** is:

\[
\boxed{62}
\]