Vectors

Math PresentationBy Marius and Samuel

Overview• Vectors in 2-dimensions

– Vectors– Operation with Vectors– Vectors in Component Form– Vector Equations– Vectors in coordinate Geometry– Parallelism– Unit Vectors– Angles and Scalar Products

• Vectors in 3-dimensions– 3-dimensional coordinates– 3-dimensional Vectors– Algebraic operations with 3-D Vectors– Parallelism– Unit Vectors– Collinear points and ratio of division – Extension– The scalar product of 3-D Vectors

• Lines in the plane and in space– Vector and parametric form of a line in 2-dimensional Geometry– The velocity vector of a moving object– Constant velocity Problems– The closest distance– Geometric application of r = a + tb– Lines in Space– Line classification

Vectors in 2-dimensions (2D)

Vectors

• Quantities which have only magnitude are called scalars.

• Quantities which have both size (magnitude) and direction are called vectors.

• Magnitude can be expressed as:– Acceleration– Force– Displacement– Momentum

Simple representation of a Vector

Vector Equality and Negative Vectors

• Two vectors are equal if they have the same magnitude AND direction.

Question

Vector Addition

Vector Subtraction

Question

Scalar Multiplication

Vectors in Composite Form

Vectors Addition

Vectors Subtraction

Scalar Multiplication and Division

Question

Lenght or Magnitude of a Vector

Component form of a Vector

Question

Scalar Products

Vectors Angle

Question

Both in IB Formula Booklet!!

In IB Formula Booklet!!

In IB Booklet

In IB Booklet

Booklet also shows the formula isolating for

In IB Booklet

Geometric Application of r=a+tb

Solution

Lines in Space

Line Classification

Last Question!

Humour time!

The vector was walking down cartesian drive when he bumped into a confused Scalar.

The vector asked him what was wrong and he replied, "Help I have no direction.“

HAHAHAHAHAHAHAHAHAHAHAHAHAHAHA