Use the dot product to find the magnitude of u if $\mathbf { u } = - 3 \mathbf { i } + 6 \mathbf { j }$
A) $\| \mathbf { u } \| = 18$
B) $\| \mathbf { u } \| =$ $6 \sqrt { 5 }$
C) $\| \mathbf { u } \| = 18$.
D) $\| \mathbf { u } \| =$ $3 \sqrt { 5 }$
E) $\| \mathbf { u } \| = 23$

Question

Use the dot product to find the magnitude of u if $\mathbf { u } = - 3 \mathbf { i } + 6 \mathbf { j }$
A) $\| \mathbf { u } \| = 18$
B) $\| \mathbf { u } \| =$ $6 \sqrt { 5 }$
C) $\| \mathbf { u } \| = 18$.
D)  $\| \mathbf { u } \| =$ $3 \sqrt { 5 }$
E) $\| \mathbf { u } \| = 23$

Quizplus · Accepted Answer

The magnitude of a vector $\mathbf{u} = a\mathbf{i} + b\mathbf{j}$ is given by $\|\mathbf{u}\| = \sqrt{a^2 + b^2}$. For $\mathbf{u} = -3\mathbf{i} + 6\mathbf{j}$, the magnitude is $\sqrt{(-3)^2 + (6)^2} = \sqrt{9 + 36} = \sqrt{45} = 3\sqrt{5}$.

Use the Dot Product to Find the Magnitude of U u=−3i+6j\mathbf { u } = - 3 \mathbf { i } + 6 \mathbf { j }u=−3i+6j

Use the Dot Product to Find the Magnitude of U $\mathbf { u } = - 3 \mathbf { i } + 6 \mathbf { j }$