# Vectors Flashcards

1
Q

Vectors are equal when?

A

Vectors are equal if they have the same magnitude and direction

2
Q

Unit vectors form

A

a

• = a1 i + a2 j + a3 k
- - -
3
Q

Component form

A

—>
PQ = u1

```             u2

u3```
4
Q

Component form for scalar product

A

a . b =
- -
( a1 x b1 + a2 x b2 + a3 x b3 )

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

5
Q

2 vectors perpendicular if…

A

a . b =
- -

` a1 x b1  + a2 x b2  + a3 x b3 = 0`
6
Q

Magnitude

A

| a1 + a2 + a3

a | = square root

7
Q

Scalar product

A

K a =
- Ku1

```                   Ku2

Ku3```
8
Q

—->
AB

Subtract
( x,y, z )

A

b - a =
x2 - x1

```          y2      -     y1

z2      -     z1```
9
Q

—->
AB

( x,y, z )

A

b + a =
x2 + x1

```          y2      +     y1

z2      +     z1```
10
Q

Cos 0

A

Cos 0 = a . b
- -
_______

```            | a | | b |
-      -```
11
Q

a. ( b + c ) = ?

- - -

A

a . b + a . c
- - - -

a . b = b . a
- - - -

12
Q

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

A

—–> ——->
AB = k BC

B is a point in common

13
Q

Section formula

A

b = n m
- _______ a + _______ c
- -
m + n m + n

14
Q

Scalar product

Evaluate a . b

A

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

```         6  x  10 x Cos 60

= 30```
15
Q

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

A

(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```
16
Q

Distance between two points

A

D = square root

( x2 - x1 )^2 + ( y2 - y1 )^2+ (z2 - z1)^2

17
Q

Angle between two vectors

A

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