Vectors

Question 1

Dot Product - Key Theory (+equation)

Answer 1

Measurement of how close two vectors are - it’s their parallel components multiplied

Equation: a . b = |a||b|cos(theta)

If Dot Product is 0 - Vectors are perpendicular (orthogonal)
If Dot Product is >0 - vectors point the same way
If Dot Product is <0 - vectors point away from each other

Question 2

Scalar Projection - Key Theory

Answer 2

Length of the shadow cast by one vector onto another vector

Question 3

Vector Projection - Key Theory

Answer 3

Creates a vector shadow that is created when one vector is cast onto another vector

Question 4

Vector Cross Product - Key Theory

Answer 4

Multplication of one vector onto another - produces a vector perpendicular to both of the other vectors

Question 5

Value of vector(a) cross vector(a)

Answer 5

0 Vector - (0,0,0)

Question 6

3D Line - Parametized Form

Answer 6

x(t) = a + pt, y(t) = b + qt, z(t) = rt
Where (a,b,c) is a point on the line
Where (p,q,r) is the components of a vector parallel to the line

Question 7

3D Line - Vector Form

Answer 7

vector_r(t) = vector_p + vector_d*t

vector_p - point on the line
vector_d - vector parallel to the line

Question 8

3D Plane - Vector Equation

Answer 8

vector_n \dot (vector_r - vector_d) = 0

Where vector_n is a vector normal to the plane
Where vector_r_ is a typical point on the plane - so unknown
Where vector_d is a point known on the plane

Question 9

Length of Vector

Answer 9

sqrt(v dot v)

Question 10

Unit Vector

Answer 10

Vector with length of 1

vector/length of vector