Vectors

Question 1

Vector

Answer 1

a quantity that has both magnitude and direction

Question 2

Scalar

Answer 2

only have magnitude

Question 3

Length on a vector

Answer 3

//u//

Question 4

Displacement

Answer 4

the distance from start to finish

Question 5

Position Vector

Answer 5

displacement from point P to origin O

Question 6

Vector Addition - Head to tail

Answer 6

Step 1: move the second vector until its tail touches the head of the first vector
Step 2: form the vector joining the tail of the first to the head of the second, this is now a+b

Question 7

Vector Addition - Parallelogram Rule

Answer 7

Step 1: move the vectors a and b until their tails collide at a common origin
Step 2: complete a parallelogram based on a and b as 2 adjacent sides
Step 3: the vector from opposite corner of the parallelogram to origin is the sum of a and b

Question 8

cosine Rule

Answer 8

a^2= b^2 + c^2 - 2bcCosA (capital letters angles)

Question 9

Sine Rule

Answer 9

a/sinA = b/sinB

Question 10

Zero Vector

Answer 10

• vector that has no magnitude

denoted by 0

Question 11

Negative of a vector

Answer 11

in the opposite direction

Question 12

addition of a negative vector to a positive

Answer 12

a+ - a = 0 vector

Question 13

When to use cosine rule

Answer 13

when you have 2 sides and 1 angle

Question 14

When to use sine rule

Answer 14

when you have 2 angles and 1 side or 2 sides and no angle

Question 15

Subtraction of Vectors

Answer 15

u - v = u+(-v)

Question 16

Vector subtraction Rule: Head to Tail

Answer 16

Step 1: Reverse the sense of v to create
Step 2: move (-V) so that its tail lies at the head of u
Step 3: join the tail of u to the head of (-v) to form u+(-v) = u - v

Question 17

Vector subtraction Rule: Tail to Tail

Answer 17

Step 1: move v parallel to itself so that its tail touches the tail of u
Step 2: draw the vector from the head of v to the tail of u, this is u-v

Question 18

When to use addition rules

Answer 18

when you want to know where youll end up

Question 19

When to use subtraction rule

Answer 19

when you want to know how you got there

Question 20

Scalar Multiplication -for s greater or equal to 0

Answer 20

the product SU is defined to be a vector in the same direction as u but with the length s times as long

Question 21

Scalar Multiplication - for s less than 0

Answer 21

su has length s times that of u but has opposite direction

Question 22

Unit Vectors

Answer 22

has the same direction of u but has the length of one unit ((1/IuI) x u)

Question 23

Angle Between Vectors

Answer 23

the lesser of the 2 possible angles between u and v

Question 24

u + v

Answer 24

v+u

Question 25

(u+V) + w

Answer 25

u + (v + w)

Question 26

u + 0

Answer 26

0 + u = u

Question 27

u + (-u)

Answer 27

0

Question 28

dot product

Answer 28

is a number denoted by u.v (length of u)(scalar component of V parallel to u) /u/ /v2/ /u/ /v/ cos0

Question 29

dot product theta

Answer 29

angle between the vectors (between 0 and 180)

Question 30

Scalar Components - V2

Answer 30

/v/ cos0 (parallel)

Question 31

Scalar Components - V1

Answer 31

/v/ sin0 (perpendicular)

Question 32

Cross Product - length

Answer 32

/UxV/ = (length of u) (scalar component of V perpendicular to u) /u/ /v/ sin0

Question 33

Cross Product - direction

Answer 33

perpendicular to both u and v

Question 34

Cross Product - sense

Answer 34

given by right hand grip rule

Question 35

coordinates in a 2D shape

Answer 35

x and y

Question 36

coordinates in a 3d shape

Answer 36

x,y and z

Question 37

orthonormal basis

Answer 37

OP = u = u1i + u2j +u3k

Question 38

Vector Addition

Answer 38

if u = u1i + u2j +u3k and v = v1i + v2j +v3k | then u+v = (u1 +v1)i + (u2 + v2)j + (u3+v3)k

Question 39

Components of zero factor

Answer 39

0i + 0j + 0k

Question 40

components of -u

Answer 40

u = u1i + u2j +u3k -u = (-1) (u1i + u2j +u3k) = - u1i - u2j - u3k

Question 41

Vector Subtraction

Answer 41

``` u = u1i + u2j +u3k and v = v1i + v2j +v3k u-v = (u1-v1)i + (u2-v2)j + (u3-v3)k ```

Question 42

Scalar Multiplication

Answer 42

su = su1i + su2j +su3k

Question 43

When to use dot product

Answer 43

for vectors

Question 44

when to use cross product

Answer 44

for scalars

Question 45

Dot product of the orthonormal basis vector

Answer 45

i x j = 0 | i x i = 1

Question 46

Dot product of arbitrary vectors in component form

Answer 46

u.v = u1v1 + u2v2 + u3v3

Question 47

Length of vector in terms of cartesian components

Answer 47

/u/ = square root of u1^2 + u2^2 = u3^2

Question 48

Angles between two vectors from cartesian component

Answer 48

cos0= u.v/ /u//v/ | = (u1v1 +u2v2 + u3v3 )/ (square root of u1^2 + u2^2 + u3^2 ) x (square root of v1^2 + v2^2 + v3^2)

Question 49

Unit Vector

Answer 49

^u = (1/ /u/)(u1i +u2j + u3k)

Question 50

Work

Answer 50

Force x length times cos0

Question 51

Unit vector

Answer 51

Divide vector formula by length

Question 52

Displacement

Answer 52

Distance from a to b

Question 53

Work (Cartesian)

Answer 53

Force x displacement

Question 54

Torque

Answer 54

R x f x sin0