Question

Determine Dot products and angle between vectors.

a) $u·v$

b) The angle between u and v to the nearest degree.

$u=i+j,v=i-j$

Short answer

a. $u·v=0$

b. $\theta =90°$

Step-by-step solution

a.Step 1. Given information.

$\begin{array}{l}\overrightarrow{u}=i+j\\ \overrightarrow{v}=i-j\end{array}$

Step 2. Determining the dot product.

The dot product of vectors

$\overrightarrow{u} .\overrightarrow{v} =a_1{b}_1+a_2{b}_2$

$\overrightarrow{u} .\overrightarrow{v} =(1\times 1)+(1\times -1)$

$\overrightarrow{u} .\overrightarrow{v} =1-1$

b.Step 1. Given information.

$\begin{array}{l}\overrightarrow{u}=i+j\\ \overrightarrow{v}=i-j\end{array}$

also from part (a) $\overrightarrow{u} ·\overrightarrow{v} =0$

Now, $\cos \theta =\frac{\overrightarrow{u} ·\overrightarrow{v} }{|\overrightarrow{u} ||\overrightarrow{v} |}$

$\cos \theta =0=90°$