11. Vectors

Question 1

How to write vector AB

Answer 1

—>

AB

Question 2

Magnitude of vector a

Answer 2

a |

Question 3

If two vectors have the same magnitude and direction

Answer 3

They are the same vector and are parallel

Question 4

Adding vectors

Answer 4

–> —> —>

AB + BC = AC but |AB| + |BC| ≠ |AC|

Question 5

0 vector

Answer 5

No displacement

Question 6

How to write a vector parallel to vector a

Answer 6

λa where λ is a scalar

Question 7

Unit vector

Answer 7

A vector whose magnitude is 1

a^2 + b^2 = 1

Question 8

Basis unit vector

Answer 8

A unit vector that is parallel with either the x or y axis

Question 9

i vector

Answer 9

( 1 )

0

Question 10

j vector

Answer 10

( 0 )

1

Question 11

Vector ci + dj

Answer 11

( c )

d

Question 12

Magnitude-direction form

Answer 12

Defining a vector by giving it’s magnitude and its angle from one of the coordinate axes (usually anti-clockwise from i)

Question 13

How to write θ if 180 < θ < 360

Answer 13

-180 < θ < 0

Question 14

a when a = (r, θ) and θ is measured anti-clockwise from positive i

Answer 14

( r cosθ)

r sinθ

Question 15

a

Answer 15

Unit vector parallel to a
a
—-
|a|

Question 16

Notation of position vector A

Answer 16

—>

OA

Question 17

How to find the position vector of A

Answer 17

Put the x and y coordinates into a vector

Question 18

—–>

How to find vector AB from position vectors

Answer 18

—-> —->

OB - OA

Question 19

Unit vector in the direction of u formula

Answer 19

u
û = ———
|u|

Question 20

Bisect

Answer 20

Cross in the middle to cut in half

Question 21

How to show the ratio a line is divided into

Answer 21

Write the same vector in different ways using scalars λ and μ for the vector it is part of the way along
Set the coefficients of a and b equal and solve

Question 22

Finding the angle between vectors

Answer 22

Form a triangle and use cosine rule with the magnitude of each

Question 23

Velocity

Answer 23

a
—– x speed
|a|