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Question:
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If the angle between the vectors $\overrightarrow{\mathbf{a}}$ and $\overrightarrow{\mathbf{b}}$ is $\frac{\pi}{3}$, what is the
angle between $-5 \overrightarrow{\mathbf{a}}$ and $6 \overrightarrow{\mathbf{b}}$ ?
Options:
angle between $-5 \overrightarrow{\mathbf{a}}$ and $6 \overrightarrow{\mathbf{b}}$ ?
Solution:
1186 Upvotes
Verified Answer
The correct answer is:
$\frac{2 \pi}{3}$
From the figure it is clear that the angle between
$6 \overrightarrow{\mathbf{b}}$ and $-5 \overrightarrow{\mathbf{a}}$ is $120^{\circ}$ or $\frac{2 \pi}{3}$
ALTERNATE SOLUTION:
$\theta=\pi-\frac{\pi}{3}=\frac{2 \pi}{3}$
$6 \overrightarrow{\mathbf{b}}$ and $-5 \overrightarrow{\mathbf{a}}$ is $120^{\circ}$ or $\frac{2 \pi}{3}$
ALTERNATE SOLUTION:
$\theta=\pi-\frac{\pi}{3}=\frac{2 \pi}{3}$
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