You have been flying in the direction 2 i + j + k for quite awhile. You are curr

Question

You have been flying in the direction 2 i + j + k for quite awhile. You are currently at the point (6, 3, 3). You discovered that there is a great place on the next approaching that delivers food. The coordinates of the food place are (8,8,8). To keep the food as hot, they put it into an insulated capsule and fire it.

1) What is the parametric equation that describes your flight path?

2) How far will your food travel from the place to the point of interception with you?

3) What is the parametric equation describing the flight path of your food?

I know the problem is very unrealistic, THANKS!

Explanation / Answer

1) parametric eqn : direction vec. : 2i+j+k pt. (6,3,3)

x=6+2t , y=3+t , z=3+t

2)distance b/w (6,3,3) & (8,8,8) = (2^2) + (5^2) + (5^2)

=54 = 7.34 units

3) flight path is eqn b/w (6,3,3) and (8,8,8)

Direction: (8-6 , 8-3 , 8-3)= (2,5,5)

Parametric eqn: x=6+2t , y=3+5t , z=3+5t

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