1. unit vector: unit vector a0= vector a/| vector a|

2.P(x, y) then vector OP=x vector i+y vector j.

| vector OP|= root sign (x square +y square)

3.P2(x2，y2)

Then the vector p 1p2 = {x2-x 1, y2-y 1}

| vector P 1P2|= radical sign [(x2-x 1) square +(y2-y 1) square]

4. Vector A = {x 1, x2} Vector B = {x2, y2}

Vector a* vector b=| vector a | | vector b | * cos α = x1x2+y1y2.

Cosα= vector a* vector b/| vector a|*| vector b|

(x 1x2+y 1y2)

Root number (x 1 square +y 1 square) * root number (x2 square +y2 square)

5. Space vector: same as above.

(Hint: Vector A = {x, y, z})

6. Necessary and sufficient conditions:

If vector a⊥ vector b

Then vector a* vector b=0

If vector a// vector b

Then vector a* vector b =+| vector a|*| vector b= |

Or x 1/x2=y 1/y2.

7. Vector A Vector b| Square

= | Vector a| Square+| Vector b| Square 2 Vector a* Vector B.

= (Vector A, Vector B) squared

Please adopt it.