Test 1

Question 1

Two vectors are parallel in the same direction if a^=

Answer 1

c*b^ and c>0

Question 2

Unit vector =

Answer 2

direction/magnitude

Question 3

Find a vector length 2 in the same direction as 3i^-4j^

Answer 3

2(unit vector for 3i^-4j^)

Question 4

How to take dot product

Answer 4

multiply corresponding components and then sum all together

Question 5

Dot product results in a…

Answer 5

scalar quantity

Question 6

The dot product helps find…

Answer 6

the angle between 2 vectors

Question 7

What equation helps find the angle between 2 vectors?

Answer 7

cos(theta) = (a^ dot b^)/(mag(a)*mag(b))

Question 8

a^ and b^ are perpendicular if

Answer 8

dot product is 0

Question 9

How to prove <2,4> and <6,-3> are orthogonal

Answer 9

Take dot product. It would equal 0.

Question 10

Statics use for cross product

Answer 10

M = r^ x F^

Question 11

det |ab/cd| =

Answer 11

ad-bc

Question 12

How to take cross product

Answer 12

i^ j^ k^ / a1^ a2^ a3^ / b1^ b2^ b3^ |
cofactor expansion
i^det-j^det+k^det

Question 13

sign for i,j,k

Answer 13

(-1)^row+column

Question 14

a^ x b^ is ______________ to the plane formed by vectors a^ and b^

Answer 14

perpendicular

Question 15

if a^ x b^ = 0, then

Answer 15

a^ is parallel to b^

Question 16

length of cross product can be calculated by

Answer 16

finding the area of the parallelogram formed by a^ and b^, which is || a^ x b^ ||

Question 17

1/2 || a^ x b^ || =

Answer 17

area of triangle formed by a^ and b^

Question 18

What do you need to plot a line in 3D?

Answer 18

Point (x1, y1, z1) and parallel vector (slope)

Question 19

What parametric equations are used to plot a line?

Answer 19

x = x1 + a1t
y = y1 + a2t
z = z1 + a3t
Point (x1, y1, z1)
Parallel vector

Question 20

How do you plot a line given two points?

Answer 20

P2-P1 gives parallel vector. Use P1 as point.

Question 21

What do you need to plot a plane in 3D?

Answer 21

1) point from shared tail

2) perpendicular vector found from cross product

Question 22

Given three points. Steps to find equation of plane:

Answer 22

1) Subtract points to find vectors
2) Take cross product of vectors (gives perpendicular vector) (n^=<i>)
3) plugs values of equation using n vector and point from shared tail
n1(x-x1)+n2(x-x2)+n3(x-x3)=0</i>

Question 23

plane point normal form

Answer 23

-18(x-3)+0(y-2)+24(z-1)=0

Question 24

plane standard form

Answer 24

-18x+24z+30=0

Question 25

Two planes are parallel if their normal vectors are…

Answer 25

parallel

Question 26

two planes are perpendicular if their normal vectors are

Answer 26

perpendicular

Question 27

Vectors associated with lines are

Answer 27

parallel

Question 28

Vectors associated with planes are

Answer 28

perpendicular

Question 29

Find the normal vector from the equation of the plane.

2x-3y-z-5=0

Answer 29

n^ = <2, -3, -1>

Question 30

How can you tell if planes are parallel or perpendicular?

Answer 30

If the normal vectors are multiples, then they are parallel. If dot product is 0, they are perpendicular.

Question 31

Which equations should you set equal to one?

Answer 31

Ellipsoid, cone, and paraboloid

Question 32

x^2+y^2=16 is what kind of equation about which axis?

Answer 32

Cylinder about the z-axis

Question 33

x=-1 in 3D is what kind of equation?

Answer 33

Plane

Question 34

What does square rooting an equation do?

Answer 34

Make it either a positive or negative half