An airplane's position vector at time t is described by the vector function ri(t) = <...

 

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An airplane's position vector at time t is described by the vector function ri(t) = < t5t+6, t3 - 8,t +1>. A flying saucer's position vector at time s is described by the vector function r(s) = < s - 4s +3,5 -1,s+2>. (a). Do the paths of the airplane and the flying saucer intersect? That is, are they ever in the same spot at possibly different times? (b). Do the airplane and the flying saucer collide? That is, are they ever in the same spot at the same time? QUESTION 5 Find a vector function that represents the curve of intersection of the parabolic cylinder y = 2 + 1 and the hyperbolic paraboloid r = y - 22. QUESTION 6 Let r(t)= < In (t + 1), sin(t-1), et >. (a). Find an equation (vector or parametric) for the tangent line to this curve at t = 1. (b). Find r"(t). An airplane's position vector at time t is described by the vector function ri(t) = < t5t+6, t3 - 8,t +1>. A flying saucer's position vector at time s is described by the vector function r(s) = < s - 4s +3,5 -1,s+2>. (a). Do the paths of the airplane and the flying saucer intersect? That is, are they ever in the same spot at possibly different times? (b). Do the airplane and the flying saucer collide? That is, are they ever in the same spot at the same time? QUESTION 5 Find a vector function that represents the curve of intersection of the parabolic cylinder y = 2 + 1 and the hyperbolic paraboloid r = y - 22. QUESTION 6 Let r(t)= < In (t + 1), sin(t-1), et >. (a). Find an equation (vector or parametric) for the tangent line to this curve at t = 1. (b). Find r"(t).