Use the dot product to find the magnitude of u if $\mathbf { u } = \langle 6 , - 2 \rangle$
A) $\| \mathbf { u } \| = 4$
B) $\| \mathbf { u } \| = 12$
C) $\| \mathbf { u } \| = 20$
D) $\| \mathbf { u } \| =$ $4 \sqrt { 10 }$
E) $\| \mathbf { u } \| =$ $2 \sqrt { 10 }$

Question

Use the dot product to find the magnitude of u if $\mathbf { u } = \langle 6 , - 2 \rangle$
A) $\| \mathbf { u } \| = 4$
B) $\| \mathbf { u } \| = 12$
C) $\| \mathbf { u } \| = 20$
D) $\| \mathbf { u } \| =$ $4 \sqrt { 10 }$
E)​ $\| \mathbf { u } \| =$ $2 \sqrt { 10 }$

Quizplus · Accepted Answer

The magnitude of a vector $\mathbf{u} = \langle a, b \rangle$ is given by $\| \mathbf{u} \| = \sqrt{a^2 + b^2}$. For $\mathbf{u} = \langle 6, -2 \rangle$, $\| \mathbf{u} \| = \sqrt{6^2 + (-2)^2} = \sqrt{36 + 4} = \sqrt{40} = 2\sqrt{10}$.

Use the Dot Product to Find the Magnitude of U u=⟨6,−2⟩\mathbf { u } = \langle 6 , - 2 \rangleu=⟨6,−2⟩

Use the Dot Product to Find the Magnitude of U $\mathbf { u } = \langle 6 , - 2 \rangle$