First slide

Straight lines in 3D

Question

A plane meets the coordinate axes A, B, C so that the centroid of the triangle ABC is (1, 3, 6). Then the equation of the plane is

Moderate

A

6x + 2y + z = 18
B

x + 6y + 2z = 18
C

x + 6y + 2z = 3
D

6x + 2y + z = 3

Solution

$(\frac{a}{3}, \frac{b}{3}, \frac{c}{3}) = (1, 3, 6)$
a = 3, b = 9, c = 18

$\frac{x}{3} + \frac{y}{9} + \frac{z}{18} = 1$

6x + 2y + z = 18

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