11.2 space coordinates and vectors in space. 3 dimensional coordinate plane
DESCRIPTION
Plotting points in 3DTRANSCRIPT
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11.2 Space coordinates and vectors in Space
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3 dimensional coordinate plane
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Plotting points in 3D
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3D coordinate systems
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The distance formula in 3-D
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Example 1
• Find the distance between points (2,-1,3) and (1,0,-2)
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Example 1 Solution
• Find the distance between points (2,-1,3) and (1,0,-2)
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Vectors in Space box
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Equation of a sphere
• Find the equation of a sphere with • Center(4,-1,1) and radius 7
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Adding unit vectors (coordinates)
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Find components of a vector by subtracting initial point from terminal point
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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)
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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
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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)
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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)
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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])
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For any job, it is important to have the right equipment.
For this class you will need a TI89 Calculator