Find the dot product of $\vec { u } = \langle 1,2,1 \rangle$ and $\vec { v } = \langle 2,2,1 \rangle$ and the cosine of the angle between them.
A) $7 , \cos ( \theta ) = \frac { 7 } { 3 \sqrt { 6 } }$
B) $7 , \cos ( \theta ) = \frac { 7 } { 54 }$
C) $9 , \cos ( \theta ) = \frac { 1 } { 6 }$
D) $6 , \cos ( \theta ) = \frac { 1 } { 9 }$

Question

Quizplus · Accepted Answer

The dot product of $\vec{u}$ and $\vec{v}$ is calculated as $1*2 + 2*2 + 1*1 = 7$. The magnitude of $\vec{u}$ is $\sqrt{1^2 + 2^2 + 1^2} = \sqrt{6}$, and the magnitude of $\vec{v}$ is $\sqrt{2^2 + 2^2 + 1^2} = \sqrt{9} = 3$. The cosine of the angle between them is $\cos(\theta) = \frac{7}{\sqrt{6} * 3} = \frac{7}{3\sqrt{6}}$.

Find the Dot Product Of u⃗=⟨1,2,1⟩\vec { u } = \langle 1,2,1 \rangleu=⟨1,2,1⟩

Find the Dot Product Of $\vec { u } = \langle 1,2,1 \rangle$