Lines&Planes: Day 5

Question 1

What is the equation of slope of a line?

Answer 1

y=mx+b

Question 2

What is the equation for the vector equation of a line?

Answer 2

r= ro + td
ro-point on the line
d- a direction vector (shows step pattern of line)
t- any # of steps

Question 3

How do you find out if a given point on a line?

Answer 3

ex. r= [1,4,7] + t [3,3,2], is the pt. [10,13,13] on the line?
- use the x values from each vector to determine what t makes x=10
- 1 + 3t=10 t=3
- sub t=3 to see if pt is on the line
- r=[1,4,7] + 3[3,3,2] =[10,13,13]
- yes its on the line

Question 4

What is a plane?

Answer 4

-need 3 (non-collinear) points to define plane

Question 5

What is the vector equation of a plane?

Answer 5

-uses a pt and 2 direction vectors
r=ro+td+sd
d1/d2=unique direction vectors
t/s= any # of steps in either direction to get to another pt

Question 6

What is the scalar equation of a plane?

Answer 6

Ax+By+Cz+D=0

-uses the normal to the plane and a point

Question 7

By definition, what does a cross product yield?

Answer 7

a result perpendicular to both original vectors

Question 8

How do you find the D value in the scalar equarion of a plane?

Answer 8

sub in given pt (x,y,z) to find D

Question 9

How do you find the y-int of the equation?

Answer 9

at y-int, x=0 z=0, so sub in 0 for x and z and solve for y

Question 10

How do you know if a given value is on the plane?

Answer 10

check if the point satifies the equation by subbing in the points for the x,y and z variables

Question 11

What happens to the D value if the plane goes through the origin? (contains a point (0,0,0))

Answer 11

The D value=0=no D value