Question

Given bold u equals left angle bracket 1 comma 3 right angle bracket and bold v equals left angle bracket 2 comma 6 right angle bracket, find 2 bold v plus bold u.
(1 point)
Responses

left angle bracket 5 comma 15 right angle bracket
Image with alt text: left angle bracket 5 comma 15 right angle bracket

left angle bracket 4 comma 12 right angle bracket
Image with alt text: left angle bracket 4 comma 12 right angle bracket

left angle bracket 3 comma 9 right angle bracket
Image with alt text: left angle bracket 3 comma 9 right angle bracket

left angle bracket 6 comma 18 right angle bracket

Answer 1

To find \( 2\mathbf{v} + \mathbf{u} \), we first need to calculate \( 2\mathbf{v} \) and then add \( \mathbf{u} \).

Given:
- \( \mathbf{u} = \langle 1, 3 \rangle \)
- \( \mathbf{v} = \langle 2, 6 \rangle \)

First, calculate \( 2\mathbf{v} \):
\[
2\mathbf{v} = 2 \cdot \langle 2, 6 \rangle = \langle 2 \cdot 2, 2 \cdot 6 \rangle = \langle 4, 12 \rangle
\]

Next, add \( \mathbf{u} \):
\[
2\mathbf{v} + \mathbf{u} = \langle 4, 12 \rangle + \langle 1, 3 \rangle = \langle 4 + 1, 12 + 3 \rangle = \langle 5, 15 \rangle
\]

Thus, the result of \( 2\mathbf{v} + \mathbf{u} \) is:
\[
\langle 5, 15 \rangle
\]

The correct answer is:
- **left angle bracket 5 comma 15 right angle bracket**