Question

The dot product is defined as |a||b|cos x where x is the angle between a and b, 0 < x < 180.

1. In the dot product definition, what happens if x > 180

2. Explain why the dot product of any vector and the zero vector is equal to zero.

3. What does the dot product measure?

Answer 1

1. What do you know of cos x when x > 180 ?

Answer 2

2. To answer this, calculate |zerovector|

Answer 3

can you explain 1 and 3?

Answer 4

1. If x > 180, say 200, then it is 20 degrees more than 180. cos 200 is the same as the cos 160 (20 less than 180).
So the dot product is the same as if the angle were 160 degrees.

How can this be? Draw two vectors with angle of 200 degrees to see what is going on...

Answer 5

3. The notation for a dot b = (a,b).
If (a, b) = |a||b|cosx, you can rewrite this as \[\cos x = \frac{ (a,b) }{ |a||b| }\]
So you can use the dot product to calculate the angle between the vectors.