# Thread: Vectors and an angle

1. ## 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.

2. 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

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

Where theta is the angle between two vectors.

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

Use the distributive property of the dot product.

3. 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"?

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.