Linear Algebra--Length and Dot Products of Vectors

1.The dot product(inner product) of v = (v1,v2) and w = (w1,w2) is the number
v·w: v·w = v1w1 + v2w2.

2.The product of perpendicular vectors is zero.

3.The dot product v·w equals w·v. The order of
v and w makes no difference.

4.To compute v·w, multiply each vi times wi. Then add.

5.The length ||v|| of a vector v is the square root of
v·v.

6.A unit vector is a vector whose length equals one. Then u·u
= 1. (i = (1, 0), j = (0, 1), u = (cosa, sina)).

7.Unit vecotr: u = v/||v|| is a unit vector in the same direction as v.