Question

Find the dot product of the two given vectors, bold u equals left angle bracket 1 comma 6 right angle bracket and bold v equals left angle bracket negative 5 comma negative 2 right angle bracket.
(1 point)
Responses

negative 17
Image with alt text: negative 17

negative 7
Image with alt text: negative 7

7
7

17

Answer 1

To find the dot product of the two vectors \(\mathbf{u} = \langle 1, 6 \rangle\) and \(\mathbf{v} = \langle -5, -2 \rangle\), we use the formula:

\[
\mathbf{u} \cdot \mathbf{v} = u_1 v_1 + u_2 v_2
\]
where \(u_1\) and \(u_2\) are the components of vector \(\mathbf{u}\) and \(v_1\) and \(v_2\) are the components of vector \(\mathbf{v}\).

Substituting the values:

\[
\mathbf{u} \cdot \mathbf{v} = 1 \cdot (-5) + 6 \cdot (-2)
\]

Calculating each part:

\[
= -5 + (-12) = -5 - 12 = -17
\]

Therefore, the dot product \(\mathbf{u} \cdot \mathbf{v} = -17\).

The correct response is **negative 17**.