Chapter 8.4-8.7 Test formulas

Question 1

Vector

Answer 1

A quantity that has magnitude and direction and is a directed line segment

Question 2

Vectors in standard form- position vector

Answer 2

V= P1 P2=

Question 3

Unit vector in 2d and 3d

Answer 3

U= v/||v||; ||u||=1

Question 4

Algebraic Vector in 2d

Answer 4

V= ||v|| cosθi + ||v|| sinθj

Question 5

Dot Product in 2d

Answer 5

v⋅w= a1a2 + b1b2

Question 6

Angle between vectors in 2d and 3d

Answer 6

cosθ= u⋅v/ ||u|| ||v||

Question 7

What does orthogonal mean?

Answer 7

Perpendicular and the dot product is 0

Question 8

What if two vectors have the same slopes?

Answer 8

They are parallel

Question 9

Work formula if no angle in 2d

Answer 9

W= ||F|| ⋅ ||vectorAB||

Question 10

Work formula if angle in 2d

Answer 10

W= F ⋅ vector AB

Question 11

Distance formula in space (3d)

Answer 11

d= √(Δx)^2 +(Δy)^2 +(Δz)^2

Question 12

Δ (delta) means what?

Answer 12

change in the variable

Question 13

Position Vectors in Space (3d)

Answer 13

V= P1P2= (x2-x1)i + (y2-y1)j + (z2-z1)k

Question 14

Dot Product in space (3d)

Answer 14

v⋅w= a1a2+ b1b2+ c1c2

Question 15

Is the dot product a value or an equation

Answer 15

a value

Question 16

General Form for a Circle in 2d

Answer 16

Standard form= (x-h)^2+ (y-k)^2= r^2. Center: (h,k). radius= r

Question 17

General form for a sphere

Answer 17

(x-x0)^2+ (y-y0)^2+ (z-z0)^2 =r^2. Center: (x0, y0, z0). Radius= r

Question 18

Direction Angles of a 3 dimensional vector

Answer 18

cos α= a/ ||v||; cos β= b/ ||v||; cos γ= c/ ||v||

Question 19

For cross product (VxW) what do you use?

Answer 19

Matrices

Question 20

What is (uxv) ⋅ u?

Answer 20

0

Question 21

What is the difference between (vxw) and (wxv)?

Answer 21

Their answers will be opposite