Vectors

Question 1

What is the vector product equ

Answer 1

|A||b|sin()= |axb|

Question 2

What is the vector product form

Answer 2

R = a + yb
R-a = yb
(R-a) x b = 0
(R x B ) = (A X B)
(R x b) = c

Question 3

Vector form of a plane

Answer 3

R = a + yb +wc

Question 4

Scalar product form of plane

Answer 4

B x c are normal to the plane so are n
(R-a) also a line on a plane when a and r are points on a plane
(R -a ) . N = 0 as they are perpendicular
R . N - a . N =0
R . N = a. N
R . (Vector) = number

Question 5

How to convert scalar product form into Cartesian

Answer 5

R.n = a.n
R.n = p
Turn r into vector x y z
Do dot product

Question 6

How to calculate the angle between a line and a plane

Answer 6

Sin() = |b.n|/ |b||a|

Question 7

Angle between 2 intersecting planes

Answer 7

Cos() = |n1.n2/|N1|N2|

Question 8

How to find a line intersecting plane and its coordinates

Answer 8

Equate the equ of the plane and equ of the line together r=r
Expand it out to get three simultainious equations to solve in the calculator
Put it back into the equ of a line to get the points of intersection

Question 9

How to find the distance from a point to a plane

Answer 9

If u have a plane AX + BY + CZ + D = 0
And the point a,b,c
|Aa + Bb + Cc + D / square root (A^2 + B^2 + C^2)|

Question 10

Distance from a plane to the origin

Answer 10

If R . N = p
|p/|n||

Question 11

Shortest distance between 2 skew lines

Answer 11

Find the vector between two points
Find the normal to the two directions
(A-b).n/|n|

Question 12

How to find the image of a pion across a plane

Answer 12

Consider a point a
And a plane t
Find a normal to the plane and call if vector f
Create a line with point a and vector f —— a + sf
Equate the line and the plane
Then expand out and get 3 simultainious equations and find s
Do A + 2SF