$\"\"$

\

The vectors are $\"\"$ and $\"\"$ .

\

(a)

\

Find the dot product $\"\"$ .

\

The dot product of the two vectors $\"\"$ and $\"\"$ is $\"\"$ .

\

Compare the vectors with general form.

\

$\"\"$ and $\"\"$ .

\

Substitute $\"\"$ and $\"\"$ in $\"\"$ .

\

$\"\"$

\

$\"\"$ .

\

The dot product of the two vectors is $\"\"$ .

\

$\"\"$

\

(b)

\

Find the angle between $\"\"$ and $\"\"$ .

\

The vectors are $\"\"$ and $\"\"$ .

\

The angle between the two vectors $\"\"$ and $\"\"$ is $\"\"$ .

\

Where $\"\"$ and $\"\"$ are magnitudes of the vectors.

\

The magnitude of the vector $\"\"$ is $\"\"$ .

\

$\"\"$ and $\"\"$ .

\

Substitute $\"\"$ and $\"\"$ and $\"\"$ in $\"\"$ .

\

$\"\"$

\

$\"\"$

\

$\"\"$ .

\

The angle between the two vectors is $\"\"$ .

\

$\"\"$

\

(c)

\

The angle between the two vectors is $\"\"$ .

\

Therefore, the two vectors are parallel.

\

$\"\"$

\

(a) The dot product of the two vectors is $\"\"$ .

\

(b) The angle between the two vectors is $\"\"$ .

\

(c) The two vectors are parallel.