3. The trajectories of two particles are given by Particle A: T (t) = (t² , 7t – 12, t²) Particle B: r (t) = (4t – 3, t² , 5t – 6) a. Do the particles ever collide? If so, at what time? b. When the particles collide, are they moving in similar directions or opposite directions? Find the angle between their tangent vectors. (Give your answer in degrees, between 0 and 180.) c. When the particles collide, which particle is moving faster? Justify your answer.
3. The trajectories of two particles are given by Particle A: T (t) = (t² , 7t – 12, t²) Particle B: r (t) = (4t – 3, t² , 5t – 6) a. Do the particles ever collide? If so, at what time? b. When the particles collide, are they moving in similar directions or opposite directions? Find the angle between their tangent vectors. (Give your answer in degrees, between 0 and 180.) c. When the particles collide, which particle is moving faster? Justify your answer.
3. The trajectories of two particles are given by Particle A: T (t) = (t² , 7t – 12, t²) Particle B: r (t) = (4t – 3, t² , 5t – 6) a. Do the particles ever collide? If so, at what time? b. When the particles collide, are they moving in similar directions or opposite directions? Find the angle between their tangent vectors. (Give your answer in degrees, between 0 and 180.) c. When the particles collide, which particle is moving faster? Justify your answer.
Particle A: r 1 → ( t ) = ⟨ t 2 , 7 t − 12 , t 2 ⟩
Particle B: r 2 → ( t ) = ⟨ 4 t − 3 , t 2 , 5 t − 6 ⟩
Do the particles ever collide? If so, at what time?
When the particles collide, are they moving in similar directions or opposite directions? Find the angle between their tangent vectors. (Give your answer in degrees, between 0 and 180.)
When the particles collide, which particle is moving faster? Justify your answer.
Transcribed Image Text:3. The trajectories of two particles are given by
Particle A: i (t) = (t², 7t – 12, t²)
Particle B: r (t) = (4t – 3, t2 , 5t – 6)
a. Do the particles ever collide? If so, at what time?
b. When the particles collide, are they moving in similar directions or opposite directions? Find the angle between their tangent vectors. (Give your answer
in degrees, between O and 180.)
c. When the particles collide, which particle is moving faster? Justify your answer.
Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.
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