Guided Example #2 - Vectors

Guided Example

Find the dot product of the vectors P and Q given that the angle between the two vectors is 45° and

$| P | = 25$ units and $| Q | = 4$ units

a. $50$
b. $50 \sqrt{2}$
c. $50 \sqrt{3}$
d. None of the above

The correct answer is B. To see why, view each of the steps below.

Using our formula from before for dot product:
$P • Q = | P | | Q | cos θ$

we have:
$P • Q = | P | | Q | cos θ$
$= 25 \times 4 \times cos 45 °$
$= 100 \times \frac{\sqrt{2}}{2}$
$= 50 \sqrt{2}$

Using our formula from before for dot product:
$P • Q = | P | | Q | cos θ$

we have:
$P • Q = | P | | Q | cos θ$
$= 25 \times 4 \times cos 45 °$
$= 100 \times \frac{\sqrt{2}}{2}$
$= 50 \sqrt{2}$