11.2 Space coordinates and vectors in Space. 3 dimensional coordinate plane

11.2 Space coordinates and vectors in Space

3 dimensional coordinate plane

Plotting points in 3D

3D coordinate systems

The distance formula in 3-D

Example 1

• Find the distance between points (2,-1,3) and (1,0,-2)

Example 1 Solution

• Find the distance between points (2,-1,3) and (1,0,-2)

Vectors in Space box

Equation of a sphere

• Find the equation of a sphere with • Center(4,-1,1) and radius 7

Adding unit vectors (coordinates)

Find components of a vector by subtracting initial point from terminal point

Parallel vectors

• Vector w has initial point (2,-1,3) and terminal point (-4,7,5). Which of the following vectors is parallel to w? Why?

• u = (3,-4,-1)• v= (-4,7,5)

Parallel vectors solution

Parallel vectors are scalar multiples of each other (that is the definition of parallel)

Vector u is parallel to the given vector because -2 times vector u equals the given vector

Example 5

Use vector to determine if the following points are collinear.

• P(1,-2,3), Q(2,1,0) and R(4,7,-6)

Example 5 SolutionUse vector to determine if the following

points are collinear.• P(1,-2,3), Q(2,1,0) • and R(4,7,-6)

Find a unit vector in the direction of v

v = 3i + 2j + k

Note: the TI 89 has this as a built in operation.

Press 2nd 5 math – 4 matrices – L vector ops- 1 unitV unitV([3,2,1])

For any job, it is important to have the right equipment.

For this class you will need a TI89 Calculator