# Vectors and an angle

• Apr 6th 2011, 08:36 AM
cottontails
Vectors and an angle
"Suppose a and b are vectors such that |a| = 3, b = 2 and the angle between a and b is (theta) = pi/3. Evaluate (a + b) . (a and b)." (Note: The '.' implying dot-product).

I am unsure with how to approach this question, considering there is also an angle involved. I am moreover unsure with how to evaluate the equation, since there are no numbers within it and it is with using the dot product. I did at first try expanding out the equation but then realised that was wrong. I really do not know what the angle implies in this question, either.
• Apr 6th 2011, 09:00 AM
TheEmptySet
Quote:

Originally Posted by cottontails
"Suppose a and b are vectors such that |a| = 3, b = 2 and the angle between a and b is (theta) = pi/3. Evaluate (a + b) . (a and b)." (Note: The '.' implying dot-product).

I am unsure with how to approach this question, considering there is also an angle involved. I am moreover unsure with how to evaluate the equation, since there are no numbers within it and it is with using the dot product. I did at first try expanding out the equation but then realised that was wrong. I really do not know what the angle implies in this question, either.

I mentioned in your post about projections the geometric defintion of the dot product that is

$\mathbf{a}\cdot \mathbf{b}=||\mathbf{a}||||\mathbf{b}||\cos(\theta )$

Where theta is the angle between two vectors.

Now what you did first is correct you must also remember $\mathbf{a}\cdot \mathbf{a}=||a||^2$

Use the distributive property of the dot product.
• Apr 6th 2011, 10:24 AM
HallsofIvy
Quote:

Originally Posted by cottontails
"Suppose a and b are vectors such that |a| = 3, b = 2 and the angle between a and b is (theta) = pi/3. Evaluate (a + b) . (a and b)." (Note: The '.' implying dot-product).

What do you mean by "a and b"?

Quote:

I am unsure with how to approach this question, considering there is also an angle involved. I am moreover unsure with how to evaluate the equation, since there are no numbers within it and it is with using the dot product. I did at first try expanding out the equation but then realised that was wrong. I really do not know what the angle implies in this question, either.