http://www.ck12.org Chapter 7. Vectors
x^2 = 492 + 252 − 2 · 49 · 25 ·cos 135◦
x≈ 68. 98 NIn order for Elaine to stay balanced, she will need to counteract this force with an equivalent force of her own in the
exact opposite direction.
Concept Problem Revisited
A bird flying due south at 10 miles an hour with a cross headwind of 2 mph heading NE would have a force diagram
that looks like this:
The angle between the bird’s vector and the wind vector is 45◦which means this is a perfect situation for the Law of
Cosines. Letx=the red vector.
x^2 = 102 + 22 − 2 · 10 · 2 ·cos 45◦
x≈ 8. 7The bird is blown slightly off track and travels only about 8.7 miles in one hour.
Vocabulary
Aresultant vectoris the vector that is produced when two or more vectors are summed or subtracted. It is also what
is produced when a single vector is scaled by a constant.
Scaling a vectormeans that the components are each multiplied by a common scale factor. For example: 4·<
3 , 2 >=< 12 , 8 >
Guided Practice
- Find the magnitude of|~a−~b|from Example A.
- Consider vector−→v =< 2 , 5 >and vector−→u =<− 1 , 9 >. Determine the component form of the following:
3 −→v− 2 −→u.