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.