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1. Consider the plane 4x+y-2z=4 and the line r(t) = < t, -2t, -tt >. a....

1. Consider the plane 4x+y-2z=4 and the line r(t) = < t, -2t, -tt >.

a. find the unit normal vector N of the plane.

b. as a function of t find the distance between r(t) and the plane.

2. Consider a fruit fly flying a room with velocity v(t) = < -sin(t), cos(t), 1 >

a. if the z = 1 + 2(pi) is the room's ceiling, where will the fly hit the ceiling?

b. if the temperature in the room is T(z) = 65 + (1/2)z2 how quickly is the temperature increasing for the fly at time t = 2.

Math   Calculus   
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Sorry for solving only 1st question, as it is advised here to solve first question in case of multiple questions.

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