Vectors

Question 1

Vectors are equal when?

Answer 1

Vectors are equal if they have the same magnitude and direction

Question 2

Unit vectors form

Answer 2

a

• = a1 i + a2 j + a3 k
  - - -

Question 3

Component form

Answer 3

—>
PQ = u1

             u2

             u3

Question 4

Component form for scalar product

Answer 4

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

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

Question 5

2 vectors perpendicular if…

Answer 5

a . b =
- -

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

Question 6

Magnitude

Answer 6

| a1 + a2 + a3

a | = square root

Question 7

Scalar product

Answer 7

K a =
- Ku1

                   Ku2

                   Ku3

Question 8

—->
AB

Subtract
( x,y, z )

Answer 8

b - a =
x2 - x1

          y2      -     y1

          z2      -     z1

Question 9

—->
AB

Addition
( x,y, z )

Answer 9

b + a =
x2 + x1

          y2      +     y1

          z2      +     z1

Question 10

Cos 0

Answer 10

Cos 0 = a . b
- -
_______

            | a | | b |
              -      -

Question 11

a. ( b + c ) = ?

- - -

Answer 11

a . b + a . c
- - - -

a . b = b . a
- - - -

Question 12

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

Answer 12

—–> ——->
AB = k BC

B is a point in common

Question 13

Section formula

Answer 13

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

Question 14

Scalar product

Evaluate a . b

Answer 14

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

         6  x  10 x Cos 60

           = 30

Question 15

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

Answer 15

(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

Question 16

Distance between two points

Answer 16

D = square root

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

Question 17

Angle between two vectors

Answer 17

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