Intersection of xy plane

Geometry Level pending

Find the point ( a , b , c ) (a, b ,c) that intersects the xy-plane given that:

x = 9 + 30 t x=9+30t

y = − 6 y=-6

z = 13 − 18 t z=13-18t

Answer in a + b + c a+b+c to 3 significant figures.


The answer is 24.7.

Kano Boom by Kano Boom , 16, Australia

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1 solution

Tom Engelsman
Feb 12, 2021

If P ( a , b , c ) P(a,b,c) is coincident with the x y − xy- plane, then z = 13 − 18 t = 0 ⇒ t = 13 18 . z = 13-18t = 0 \Rightarrow t = \frac{13}{18}. This also gives us x = 9 + 30 ( 13 18 ) = 92 3 x = 9 + 30(\frac{13}{18}) = \frac{92}{3} and the final point P ( 92 3 , − 6 , 0 ) ⇒ 92 3 − 6 + 0 = 74 3 = 24.67 . P(\frac{92}{3},-6,0) \Rightarrow \frac{92}{3} - 6 + 0 = \frac{74}{3} = \boxed{24.67}.

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