Vectors

Question 1

What is the scalar product of two vectors?

Answer 1

Question 2

Answer 2

Question 3

What is important about the angle that must be considered in the door scalar method?

Answer 3

Angle of both vectors leaving a point

Question 4

Answer 4

Question 5

What is the dot product of 2 vectors that are perpendicular?

Answer 5

Question 6

Answer 6

Question 7

What is a position vector?

Answer 7

(Directions how to get onto the line) - vector of a point on a line

denoted as a

Question 8

What is a direction vector?

Answer 8

(Gradient) how to move up and down a line

denoted as b

Question 9

What is the vector equation for a line in 3D?

Answer 9

Question 10

Answer 10

Question 11

What is the vector CD?

Answer 11

C—>D = d-c

Question 12

Answer 12

Question 13

What is the Cartesian equation of a line general form from the vector equation of a line?

Answer 13

Question 14

Answer 14

Question 15

What is the vector equation for a plane?

Answer 15

Question 16

Answer 16

Question 17

What is the Cartesian equation of a plane (in 3D) ?

Answer 17

Question 18

What is the geometric interpretation of d in the Cartesian equation of a plane ?

Answer 18

If a, b ,c are the same then the planes are parallel, d determines the location of the plane. The normal vector (a, b,c) determines the direction

Question 19

how do you calculate the angle between two lines?

Answer 19

1. look at the direction vectors of two lines
2. scalar product

Question 20

how do you calculate the angle between 2 planes?

Answer 20

1. look at the normal vector of the two planes
2. scalar product

make sure you give acute angle (180 - x) if asked

Question 21

Answer 21

Question 22

Answer 22

Question 23

Answer 23

Question 24

2 equations one point given

Answer 24

Question 25

Answer 25

Question 26

what are the 5 possible ways within which 3 planes can intersect?

Answer 26

1. all 3 planes parallel
2. 2 planes parallel and one cutting through
   (no planes parallel)
3. all points intersect at 1 point
4. sheaf: all 3 planes share a common line
5. triangular prisim: 3 pairs of straight lines are all parallel

Question 27

what does a sheaf look like?

Answer 27

Question 28

what does a triangular prism look like?

Answer 28

Question 29

How do you determine which of the 5 possible scenarios of intersections are taking place for the 3 planes?

Answer 29

Question 30

Answer 30

Question 31

Answer 31

Question 32

Answer 32

Question 33

Answer 33