Find v · u.
-$\mathbf { v } = \left\langle \frac { 1 } { \sqrt { 2 } } , \frac { 1 } { \sqrt { 2 } } \right\rangle$ and $\mathbf { u } = \left( \frac { 1 } { \sqrt { 2 } } , \frac { - 1 } { \sqrt { 2 } } \right)$
A) $\frac { 1 } { \sqrt { 2 } } \mathbf { i } - \frac { 1 } { \sqrt { 2 } } \mathbf { j }$
B) 0
C) $\frac { 2 } { 2 }$
D) $\frac { 2 } { \sqrt { 2 } } \mathbf { i } - \frac { 2 } { \sqrt { 2 } } \mathrm { j }$

Question

Quizplus · Accepted Answer

The dot product of vectors $\mathbf{v}$ and $\mathbf{u}$ is calculated as $\left(\frac{1}{\sqrt{2}} \cdot \frac{1}{\sqrt{2}}\right) + \left(\frac{1}{\sqrt{2}} \cdot \frac{-1}{\sqrt{2}}\right) = \frac{1}{2} - \frac{1}{2} = 0$.

Find V · U v=⟨12,12⟩\mathbf { v } = \left\langle \frac { 1 } { \sqrt { 2 } } , \frac { 1 } { \sqrt { 2 } } \right\ranglev=⟨2​1​,2​1​⟩

Find V · U $\mathbf { v } = \left\langle \frac { 1 } { \sqrt { 2 } } , \frac { 1 } { \sqrt { 2 } } \right\rangle$