Ch.8 Vectors

1. Magnitude of vectors:

1.1. square root of : (x2-x1)^2 + (y2-y1)^2

2. Unit vector:

2.1. u = (1/ lvl ) v

3. Linear combination:

3.1. i = 〈1, 0〉 and j = 〈0, 1〉

4. Component form (angle):

4.1. v= <vcos(angle), vsin(angle)>

5. Direction angle:

5.1. tan(angle) = b/a

6. Midpoint:

6.1. M(x1+x2/2, y1+y2/2 , z1+z2/2)

7. Types of vectors:

7.1. •Parallel vectors have the same or opposite direction but not necessarily the same magnitude. • Equivalent vectors have the same magnitude and direction. • Opposite vectors have the same magnitude but opposite direction.

8. Component form of a vector:

8.1. 〈x2-x1, y2-y1〉

9. Dot product:

9.1. v1 . v2 = 〈a1,b1〉. 〈a2,b2〉 = a1.a2 + b1.b2

9.2. two vectors with a dot product of 0 are orthogonal.

10. Angle between two vectors:

10.1. cos(angle)= a . b/ lal lbl

11. Projection:

11.1. ProjvU = (u . v /lvl^2 ) v

12. Distance:

12.1. AB = square root of ((x2-x1)^2 + (y2-y1)^2 + (z2-z1)^2)