Find the angle (round to the nearest degree) between the vectors.
< -8.9, 15 > and < 14.8, -12.8 >

Question

Find the angle (round to the nearest degree) between the vectors. < -8.9, 15 > and < 14.8, -12.8 > A) 162° B) -72° C) -324 D) no solution

Quizplus · Accepted Answer

The angle between two vectors can be found using the dot product formula: $\theta = \cos^{-1}\left(\frac{a \cdot b}{\|a\|\|b\|}\right)$, where $a \cdot b$ is the dot product of vectors $a$ and $b$, and $\|a\|$ and $\|b\|$ are the magnitudes of vectors $a$ and $b$, respectively. For vectors $\langle -8.9, 15 \rangle$ and $\langle 14.8, -12.8 \rangle$, the dot product is $(-8.9)(14.8) + (15)(-12.8)$, and the magnitudes are $\sqrt{(-8.9)^2 + 15^2}$ and $\sqrt{14.8^2 + (-12.8)^2}$, respectively. Plugging these into the formula and solving for $\theta$ gives an angle close to 162° when rounded to the nearest degree.

Find the Angle (Round to the Nearest Degree) Between the Vectors