Chapter 13 – Vector Functions 13.1 Vector Functions and Space Curves 1 Objectives: Use vector -valued functions to describe the motion of objects through.
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Chapter 13 – Vector Functions13.1 Vector Functions and Space Curves
13.1 Vector Functions and Space Curves
Objectives: Use vector -valued
functions to describe the motion of objects through space
Draw vector functions and their corresponding space curves
parametric equations for the line segment that joins P to Q.
P (-2, 4, 0)
Q (6, -1, 2)
13.1 Vector Functions and Space Curves
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Example 4 – pg. 846 # 29At what points does the curve
intersect the paraboloid ?
2( ) (2 )t t t t r i k2 2z x y
13.1 Vector Functions and Space Curves
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Example 5 – pg 847 # 47If two objects travel through space along two
different curves, it’s often important to know whether they will collide. (Will a missile hit its moving target? Will two aircraft collide?) The curves might intersect, but we need to know whether the objects are in the same position at the same time. Suppose the trajectories of the two particles are given by the vector functions
for t0. Do the particles collide?
2 2 21 2( ) ,7 12, ( ) 4 3, ,5 6t t t t t t t t r r
13.1 Vector Functions and Space Curves
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More Examples
The video examples below are from section 13.1 in your textbook. Please watch them on your own time for extra instruction. Each video is about 2 minutes in length. ◦Example 3◦Example 6