The Dot Product: Examples

1. Find the Dot Product of the two vectors: <4,2,5>  <0,2,5>.

Anwser:

To do this, we must activate the vector package in Maple:

>	with(VectorCalculus);

Then it is simple:

>	<4,2,5>.<0,2,5>

2.Using the Dot Product, find the angle between the two vectors: <1,1,1>, <-4,2,-7>.

Anwser

First, find the magnitude of each vector:

>	sqrt((1)^2+(1)^2+(1)^2);

>	sqrt((-4)^2+(2)^2+(-7)^2);

Then find the dot product of the vectors:

>	<1,1,1>.<-4,2,-7>;

Then, simply follow the fomula for the angle:

>	solve(cos(x)=(-9)/(3^(1/2)*69^(1/2)),x)

3. Find the vector projection of <1,5,-3> onto <3,-2,5>.

Anwswer:
First, find the magnitude of the second vector:

>	sqrt((3)^2+(-2)^2+(5)^2);

Then find the dot product:

>	<1,5,-3> . <3,-2,5>;

Then simply put it in the formula:

>	(-22/38^(1/2))*(<3,-2,5>/38^(1/2))