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