12.5

Question 1

Vector equation of a line in R³

Answer 1

r = r₀ + tv

Question 2

Parametric equations of a line in R³

Answer 2

x = x₀ + at

y = y₀ + bt

z = z₀ + ct

Question 3

Symmetric equations of a line in R³

Answer 3

Question 4

Vector equation of a plane

Answer 4

Question 5

Scalar equation of a plane

Answer 5

Question 6

Linear equation of a plane

Answer 6

ax + by + cz + d = 0

Question 7

Lines that do not intersect and are not parallel

Answer 7

Skew lines

Question 8

How to show that lines are not skew.

Answer 8

Show that the direction vectors aren’t parallel.

Show that there are no intersections by setting each component of their parametric equations equal to each other.

Question 9

What do you need to find the equation of a plane?

Answer 9

Point and normal vector

Question 10

What do you need to find the equation of a line?

Answer 10

point and direction vector

Question 11

Answer 11

Question 12

Answer 12

Question 13

The angle between the normal vectors of 2 planes is equal to…

Answer 13

The angle between the planes

Question 14

Distance from a point to a plane formula

Answer 14

Question 15

Answer 15

Question 16

What is the distance from a point to a plane in terms of projection?

Answer 16

Question 17

Colinear vectors…

Answer 17

Lie on the same line

Question 18

Equation of line segment joining 2 points

Answer 18

r(t) = (1-t)r₀ + tr₁