r(1) = <2 +?- 21, -2 – 3,7 +1>, 1 > 0. (a) Find the time to > 0 at which the particle crosses the plane x +y 0. (b) At some time t > 0, the velocity of the particle has the same direction as the vector

Linear Algebra: A Modern Introduction
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ISBN:9781285463247
Author:David Poole
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Chapter6: Vector Spaces
Section6.6: The Matrix Of A Linear Transformation
Problem 6AEXP
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A particle starts moving at time t  =  0 and its position at time t is given by the vector function

r(t)  =  < 2t3 + t2 − 2t, −2t3 − 3, t2 + t >,    t  ≥  0.



(a) Find the time t0  >  0 at which the particle crosses the plane x + y  =  0.
(b) At some time t1  >  0, the velocity of the particle has the same direction as the vector

u  =  < 1, −3, 4 >.

Find t1.
Problem #7: A particle starts moving at time t = 0 and its position at time t is given by the vector function
[4 marks]
r(t) = <2r +? - 21, -21 – 3, 7 + t>, t> 0.
(a) Find the time to > 0 at which the particle crosses the plane x+y = 0.
(b) At some time t > 0, the velocity of the particle has the same direction as the vector
u = <1,-3, 4>.
Find t1.
Enter your answer symbolically,
as in these examples
Problem #7(a):
Enter your answer symbolically,
as in these examples
Problem #7(b):
Transcribed Image Text:Problem #7: A particle starts moving at time t = 0 and its position at time t is given by the vector function [4 marks] r(t) = <2r +? - 21, -21 – 3, 7 + t>, t> 0. (a) Find the time to > 0 at which the particle crosses the plane x+y = 0. (b) At some time t > 0, the velocity of the particle has the same direction as the vector u = <1,-3, 4>. Find t1. Enter your answer symbolically, as in these examples Problem #7(a): Enter your answer symbolically, as in these examples Problem #7(b):
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