QUESTION 1

Normalized Vector

Choose one 4 points

What are the magnitude and normalized vector , ^v=vv , of v=(1,2,2) ?

v=3 ,^v=(13,23,23)

v=5 ,^v=(15,25,25)

v=9 ,^v=(19,29,29)

QUESTION 2

Parallel Vectors

Choose one 4 points

Which of the two vectorsp andq are parallel ?

p=(2,7,1) and q=(0,14,2)

p=(6,9,15) and q=(2,3,5)

p=(1,6,4) and q=(0,3,2)

QUESTION 3

Building a Vector From two Vertices(points)

Choose one 4 points

Find the vector between the verticesA=(1,1,0) , B=(2,1,1)andtheir distance||AB||

AB=(3,2,1) and AB=14

AB=(1,0,1) and AB=2

AB=(1,0,1) and AB=2

QUESTION 4

Vectors Addition

Choose one 4 points

Given thefollowing vectors a=(2,0,1) andb=(1,2,1),

calculate2a+3b

2a+3b=(0,0,0)

2a+3b=(1,6,1)

2a+3b=(1,6,1)

QUESTION 5

3D Vectors Dot Product

Choose one 4 points

Calculate the dot product ofa=(2,1,3) and b=(0,1,3)

3

8

2

QUESTION 6

Angle Between two Vectors

Choose one 4 points

Calculate the angle between the two vectorsa=(1,2,0) andb=(4,2,1)

0

90

45

QUESTION 7

Type of Angle Between two Vectors

Choose one 4 points

find the type of angle between a=(0,-1, 3 ) and b=(1, 4 , 1).

acute angle

obtuse angle

Right right

QUESTION 8

Orthogonal or Perpendicular Vectors

Choose one 4 points

• Which two vectorsa andb are orthogonal (perpendicular) ?

a=(2,1,3) and b=(0,3,1)

a=(1,2,0) and b=(2,1,0)

a=(0,1,3) and b=(0,1,1)

QUESTION 9

Component and Projection of a vector onto another vector

Choose one 4 points

Givena =(1,2,2) and b =(1,1,1) , calculatecompaband projab

compab=3 and projab=(1,2,2)

compab=53 andprojab=(53,53,53)

compab=3 andprojab=(13,13,13)

QUESTION 10

Cross Product of two Vectors

Choose one 4 points

Calculate the cross product of a=(2,1, 3)andb=(0, 1 , 3), ab

ab=(0,1,9)

ab=(0,6,2)

ab=(6,0,2)

QUESTION 11

Vectors Differentiation

Choose one 4 points

Calculate dadt, Givena=(t2,t,2)

dadt=(2t,1,2)

dadt=(t,1,0)

dadt=(2t,1,0)

QUESTION 12

Partial Derivative of Vectors

Choose one 4 points

Calculate ux and2uyxGivenu=(ux,uy,uz)=(xy2,4+x,x2y)

ux=(1,1,2x) and 2uyx=(0,0,0)

ux=(y2,1,xy) and 2uyx=(2y,0,x)

ux=(y2,1,2xy) and 2uyx=(2y,0,2x)

QUESTION 13

Integration of Vectors

Choose one 4 points

Calculate10a(t)dt wherea=3t2i+4t3j+2k

10a(t)dt=i+j+2k=(1,1,2)

10a(t)dt=i+j=(1,1,0)

10a(t)dt=3i+4j+2k=(3,4,2)

QUESTION 14

Homogeneous System of linear Equations

Choose one 4 points

Identify the homogeneous system of linear equations.

x+yz=22x+3y+z=1xy+2z=0

x+3yz=0x+y+z=0xy+2z=0

x+yz=13y+z=0z=0

QUESTION 15

Free Variables and leading unknowns (pivots)

Choose one 4 points

Identify the free variables and the leading unknowns in{x+yz=13y+z=0

Free variables : z , leading unknowns : x and y

Free variables: none , leading unknowns : x,y and z

Free variables: x,y and z , leading unknowns : none

QUESTION 16

Gaussian Elimination

Choose one 4 points

Solve the system of linear equationsusing Gaussian elimination

x+3yz=72x+3y+z=83xy+2z=1

x=5 , y=2 , z=4

x=1, y=1 and z=3

x=1,y=2, and z=0

QUESTION 17

Consistent System of linear Equations

Choose one 4 points

Identify the consistence system of linear equations

x+yz=12x+3y+z=6xy+2z=2

x+3yz=5x+3y+8z=00z=6

x+yz=13y+z=00z=4

QUESTION 18

Inconsistent System of linear Equations

Choose one 4 points

Identify the inconsistence system of linear equations

x+yz=12x+3y+z=6xy+2z=2

x+3yz=5x+3y+8z=00z=0

x+yz=13y+z=00z=4

QUESTION 19

Linear Combination

Choose one 4 points

Identify the linear combination ofw=(3,4)in term ofu=(1,0) and v=(0,2)

w=3u+v

w=3u2v

w=3u+2v

QUESTION 20

Linear Independence

Choose one 4 points

Which two vectors are linearly independent ?

a=(1,1) and b=(4,3)

a=(1,3) and b=(2,6)

a=(2,3) and b=(0,0)

QUESTION 21

Linear Dependence

Choose one 4 points

Which vectors are linearly dependent ?

a=(1,2) and b=(2,3)

a=(1,1) and b=(4,4)

a=(1,2) and b=(2,5)

QUESTION 22

Basis of a Vector Space

Choose one 4 points

Which vectors form a basis for the given setR2

a=(1,1) and b=(3,4) for R2

a=(6,4) and b=(12,8) for R2

a=(1,5) and b=(0,0) for R2

QUESTION 23

Dimension of a Vector Space

Choose one 4 points

What is the dimension of the basis {a,b,c }={(1,1,0),(1,2,1),(1,1,1)}

dim(B)=2

dim(B)=3

dim(B)=1

QUESTION GROUP 24

Inner Product Space

Group 2 questions

QUESTION 24.1

Inner Product of Vectors

Choose one 4 points

If a=(2,0,1)and a=(1,2,1) , compute their inner producta,b

a,b=1

a,b=3

a,b=0

QUESTION 24.2

Inner Product as an Integral of two Functions

Choose one 4 points

Givenf(x)=x andg(x)=3x+2 with inner productf,g=10f(x)g(x)dx , findf,g

f,g=0

f,g=1

f,g=2

it's multiple choose.