# Vectors Flashcards

Vectors are equal when?

Vectors are equal if they have the same magnitude and direction

Unit vectors form

a

- = a1 i + a2 j + a3 k

- - -

Component form

—>

PQ = u1

u2 u3

Component form for scalar product

a . b =

- -

( a1 x b1 + a2 x b2 + a3 x b3 )

a . b = | a | x | b | cosO

- -

2 vectors perpendicular if…

a . b =

- -

a1 x b1 + a2 x b2 + a3 x b3 = 0

Magnitude

| a1 + a2 + a3

a | = square root

Scalar product

K a =

- Ku1

Ku2 Ku3

—->

AB

Subtract

( x,y, z )

b - a =

x2 - x1

y2 - y1 z2 - z1

—->

AB

Addition

( x,y, z )

b + a =

x2 + x1

y2 + y1 z2 + z1

Cos 0

Cos 0 = a . b

- -

_______

| a | | b | - -

a. ( b + c ) = ?

- - -

a . b + a . c

- - - -

a . b = b . a

- - - -

Points A, B and C are said to be Collinear if

—–> ——->

AB = k BC

B is a point in common

Section formula

b = n m

- _______ a + _______ c

- -

m + n m + n

Scalar product

Evaluate a . b

a . b = | a | | b | Cos 0

6 x 10 x Cos 60 = 30

Special cases

1 + 2

These converse statements are true and are important if the scalar product of two vectors is 0, then the two vectors are perpendicular

(1) a . b = | a | | b | Cos 90

Then as cos 90 = 0, a.b = 0

(2) a . a = | a | | b | Cos 0

Then as cos 0 = 1 a . a = |a|^2