VECTORS

Geometric Vectors

Scalars

Vectors

Equal Vectors

Opposite Vectors

Zero Vectors

Triangle law of addition

Parallelogram law

Difference between vectors

Commutative property

Associative property of addition

distributive property of addition

Position Vectors

Points of vectors (X, Y) / (X, Y, Z)

Different planes in R3 such as the XY plane or the YZ plane or the XZ

Addition using component form

Scalar multiplication using components

Using Pythagorean theorem to define two points

Addition of vectors using a method such as the parallelogram law

Finding position vectors in R3

vectors in the form a(scalar)i(vector + b(scalar)j(vector) in R2

vectors in the form a(scalar)i(vector + b(scalar)j(vector) + c(scalar)k(vector) in R2

Vectors can be expressed as forces and velocity

resultant and composition of forces yields combined force

Equilibrant of multiple forces

Angle x must be from 0 to 180 degrees

Vectors should be placed tail to tail

Tells us the amount of force applied in the direction of motion

Finds the orthogonal of the vectors

Multiple methods are available for you to find the cross product. Find which one works best for you!

Projection of one vector onto another. You can think of it kind of like a shadow

Direction Angles

A real life application includes computer animation.

Calculating work done

dot product is used when installing solar panels

Finding torque

To find equations of lines we must be given two distinct points/one point along with a direction vector

Derived from parametric equations

Written in the form: Ax + By + C = 0

Written in the form: Ax + By + Cz + D = 0

need a point and a vector to derive the equation

Can be determined in 4 ways

These equations can allow us to obtain any point on the plane

Using a line and multiple points we can come up with the equation of a plane