Exercises for Question Type 3: Determining whether two objects intersect for their given trajectory

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Exercises for Question Type 3: Determining whether two objects intersect for their given trajectory - IB

Question 1

For the moving points P_{1} (t) = 214 + t 591 and P_{2} (t) = 101 + t 872, find the time t at which the points are closest to each other.

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Question 2

For the points P_{1} (t) = (0, 0, 0) + t (1, 2, 3) and P_{2} (t) = (3, 1, 0) + t (4, - 1, 2), determine the time t at which the distance between them is minimal.

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Question 3

Determine whether the lines r_{1} = 123 + t 257 and r_{2} = 345 + s 431 intersect.

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Question 4

Find the time t at which P_{1} (t) = 111 + t 201 and P_{2} (t) = 023 + t 13 - 1 are closest.

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Question 5

Find the value of m for which the lines r_{1} = 521 + t m 34 and r_{2} = 253 + s 4 - 1 2 intersect.

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Question 6

Find the minimum distance between the points P_{1} (t) = (0, 0, 0) + t (1, 2, 3) and P_{2} (t) = (3, 1, 0) + t (4, - 1, 2) .

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Question 7

Find the value of m such that the lines r_{1} = 230 + t 11 m and r_{2} = 041 + s 312 intersect.

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Question 8

Determine whether the lines with equations r_{1} = 214 + t 591 and r_{2} = 101 + s 872 intersect.

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Question 9

Consider two points, P_{1} and P_{2}, such that the displacement vector from P_{1} to P_{2} at time t is given by d (t) = 1 - 3 t 1 + 2 t 3 - t where t \in R .

Determine the minimum distance between P_{1} and P_{2} .

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Question 10

Determine whether the lines r_{1} = 0 - 1 2 + t 341 and r_{2} = 213 + s 652 intersect.

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Question 11

Determine the value of m such that the lines r_{1} = 102 + t 3 m 5 and r_{2} = 241 + s 613 intersect.

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IB Mathematics Applications & Interpretation Question Type 3: Determining Whether Two Objects Intersect for Their Given Trajectory Exercises