Vectors

Question 1

Which process of combinging vectors is commuatative

Answer 1

Adding
Dot product

Question 2

What is a position vector compared to a displacement vecotr

Answer 2

position: describes positon from arbitrary reference point
OP=p
OR=r

displacement vector: describes position between vectors
PR=p-r

Question 3

What is the equation for a moment of a vector

Answer 3

M = r x F

Question 4

What is the equation for the magnitude of the moment of a vector

Answer 4

|M| = r x F x sinθ

Question 5

What is the unit vector equation

Answer 5

â =a/|a|

Question 6

What is the dot product equation

Answer 6

a·b=|a||b|cosθ
a·b=a₁b₁+a₂b₂+a₃b₃

Question 7

What does the dot product used for

Answer 7

scaling 2D vectors

Question 8

Dot product: when are vectors orthogonal

Answer 8

a·b=0
or a=0
or b=0

Question 9

Dot product: what does it mean if cosθ or dot product is positive

Answer 9

acute angle θ

Question 10

What is the cross product used for

Answer 10

creates a vector orthgonal to a and b
Vector product between 2 vectors

Question 11

What is the cross product equation

Answer 11

axb=|a||b|sinθn̂
or do chessboard matrix

Question 12

Cross product : when are vectors=0

Answer 12

axb=0
or a=0
or b=0
or sinθ=0 (parallel or antiparallel vectors)

Question 13

True of false: axb=bxa

Answer 13

False: axb=-(bxa)

Question 14

what is |a|=

Answer 14

=√(a·a)

Question 15

Cross product: when are vectors orthognal

Answer 15

sinθ=1
axb=|a||b|