Question

Find one third bold u, if bold u equals left angle bracket 1 comma negative 3 right angle bracket.
(1 point)
Responses

left angle bracket 1 comma negative 1 right angle bracket
Image with alt text: left angle bracket 1 comma negative 1 right angle bracket

left angle bracket one third comma negative 1 right angle bracket
Image with alt text: left angle bracket one third comma negative 1 right angle bracket

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

left angle bracket 1 comma negative 9 right angle bracket

Answer 1

To find one third of the vector **u**, given that **u** = ⟨1, -3⟩, you will need to multiply each component of the vector by \(\frac{1}{3}\).

So, let's do the calculations:

\[
\text{One third of } \mathbf{u} = \frac{1}{3} \cdot \langle 1, -3 \rangle = \langle \frac{1}{3} \cdot 1, \frac{1}{3} \cdot -3 \rangle = \langle \frac{1}{3}, -1 \rangle
\]

Thus, one third of **u** is ⟨\(\frac{1}{3}\), -1⟩.

From the options you listed, the correct response is:

**left angle bracket one third comma negative 1 right angle bracket**.