Question

Given the dot product bold w dot bold w equals 29, find the magnitude of w.
(1 point)
Responses

21
21

29
29

start root 21 end root
Image with alt text: start root 21 end root

start root 29 end root

Answer 1

The dot product of a vector \(\mathbf{w}\) with itself is equal to the square of its magnitude. This can be expressed mathematically as:

\[
\mathbf{w} \cdot \mathbf{w} = |\mathbf{w}|^2
\]

Given that \(\mathbf{w} \cdot \mathbf{w} = 29\), we can find the magnitude of \(\mathbf{w}\) as follows:

\[
|\mathbf{w}|^2 = 29
\]

To find \( |\mathbf{w}| \), we take the square root of both sides:

\[
|\mathbf{w}| = \sqrt{29}
\]

Therefore, the magnitude of \(\mathbf{w}\) is \(\sqrt{29}\).

The correct response is:

\(\sqrt{29}\)