https://file.aiquickdraw.com/mathbot/file/1726567453361zxc2oaco.jpg

The problem in the image involves vector addition and uses the law of cosines. Here's the breakdown of the information given:

1. Vectors \( \overrightarrow{OA} = a \) and \( \overrightarrow{OB} = b \), with magnitudes \( |a| = |b| = 4 \).
2. The angle between vectors \( a \) and \( b \), \( \angle AOB \), is 60°.

We are tasked with finding the magnitude \( |\overrightarrow{a} + \overrightarrow{b}| \), the magnitude of the sum of the vectors.

### Solution:

We can use the law of cosines for the magnitude of the resultant vector. The formula for the magnitude of the sum of two vectors \( a \) and \( b \) when the angle \( \theta \) between them is given is:

\[
|\overrightarrow{a} + \overrightarrow{b}| = \sqrt{|a|^2 + |b|^2 + 2|a||b|\cos(\theta)}
\]

Given:
- \( |a| = |b| = 4 \)
- \( \theta = 60^\circ \)
- \( \cos(60^\circ) = 0.5 \)

Substitute these values into the formula:

\[
|\overrightarrow{a} + \overrightarrow{b}| = \sqrt{4^2 + 4^2 + 2 \cdot 4 \cdot 4 \cdot \cos(60^\circ)}
\]
\[
|\overrightarrow{a} + \overrightarrow{b}| = \sqrt{16 + 16 + 2 \cdot 4 \cdot 4 \cdot 0.5}
\]
\[
|\overrightarrow{a} + \overrightarrow{b}| = \sqrt{16 + 16 + 16} = \sqrt{48}
\]
\[
|\overrightarrow{a} + \overrightarrow{b}| = 4\sqrt{3} \approx 6.93
\]

Thus, the magnitude of \( \overrightarrow{a} + \

If vector OA = a, vector OB = b, and |a| = |b| = 4, with the angle between them, ∠AOB = 60°, find the magnitude of vector a + vector b.

This problem involves finding the magnitude of the sum of two vectors with equal magnitudes and an angle of 60° between them. The solution uses the law of cosines to calculate the magnitude, yielding a result of approximately 6.93.

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