Finals

Question 1

Formula for distance between a point and a plane

Answer 1

X0,Y0,Z0 is our point

Question 2

How to determine if planes are parallel?

Answer 2

As an example 2x-y+z= 1. N vector is (2, -1, 1), if the other planes n vector is the same or multiples of each other, they are paralell.

Question 3

Formula to determine distance between two planes?

Answer 3

Take your two plane equations: example: 2X-Y+Z = 1

Sub in any point as long as it satisfies = 1

x0,y0,z0 = this point.

Then use the point in the regular distance formula for a plane

Question 4

How to determine orthonagality?

Answer 4

Dot product = 0

n*n

Question 5

How to determine is 3 vectors lie on the same plane

Answer 5

If the scalar triple product =0 U*(VXW)

Question 6

How do you find a unit vector?

Answer 6

Divide the vector by it’s magnitude.

Find magnitude by root a+b+c

u = v/|v|

Question 7

Find the plan parallel to L1(-2,-4,2) and L1(1,1,-1), passing through point (1,2,3)

Answer 7

1. Cross product directional vectors for L 1 and 2.
2. You will now have the required plane (2,0,2)
3. 2X+2Z = d
4. Now sub in the ponts 2+6 = 8 (d)
5. 2x+2Z = 8

Question 8

What is the direction vector of X = 3-2t Y = 3-4t Z = 2t

Answer 8

(-2,-4,2)

Question 9

What is the formula for area of a traingle?

Answer 9

AB X AC * 1/2

Question 10

Area of a parallelogram

Answer 10

AB X AC

Question 11

Volume of Parallelpiped

Answer 11

Scalar trip product

or determinate of all three (like a cross product)