Question

Two vectors drawn.Two vectors are drawn on a coordinate plane. Vector v has an initial point left-parenthesis negative 2 comma 3 right-parenthesis and terminal point left-parenthesis 4 comma 4 right-parenthesis. Vector u has an initial point left-parenthesis 4 comma negative 2 right-parenthesis and terminal point left-parenthesis 5 comma 3 right-parenthesis.
Question
Use the image to answer the question.

Find the components of vector v.
(1 point)
Responses

bold v equals left angle bracket 9 comma 1 right angle bracket
Image with alt text: bold v equals left angle bracket 9 comma 1 right angle bracket

bold v equals left angle bracket negative 5 comma 3 right angle bracket
Image with alt text: bold v equals left angle bracket negative 5 comma 3 right angle bracket

bold v equals left angle bracket 6 comma 1 right angle bracket
Image with alt text: bold v equals left angle bracket 6 comma 1 right angle bracket

bold v equals left angle bracket 5 comma 7 right angle bracket
Image with alt text: bold v equals left angle bracket 5 comma 7 right angle bracket
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Answer 1

To find the components of vector \( \mathbf{v} \), we can use the formula for the components of a vector based on its initial point \((x_1, y_1)\) and terminal point \((x_2, y_2)\):

\[
\mathbf{v} = \left< x_2 - x_1, y_2 - y_1 \right>
\]

For vector \( \mathbf{v} \):
- Initial point: \((-2, 3)\)
- Terminal point: \((4, 4)\)

Now we calculate the components:

1. \( x_2 - x_1 = 4 - (-2) = 4 + 2 = 6 \)
2. \( y_2 - y_1 = 4 - 3 = 1 \)

Thus, the components of vector \( \mathbf{v} \) are:

\[
\mathbf{v} = \left< 6, 1 \right>
\]

Therefore, the correct response is:

**bold v equals left angle bracket 6 comma 1 right angle bracket**