11 2 Space coordinates and vectors in Space

11. 2 Space coordinates and vectors in Space

3 dimensional coordinate plane

Plotting points in 3 D

3 D 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 Solution Use 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 = 3 i + 2 j + k Note: the TI 89 has this as a built in operation. Press 2 nd 5 math – 4 matrices – L vector ops - 1 unit. V([3, 2, 1])

For any job, it is important to have the right equipment. For this class you will need a TI 89 Calculator