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Question

Question: The equation of the plane through the origin containing the line \(\frac{x - 1}{5} = \frac{y - 2}{4}...

The equation of the plane through the origin containing the line x15=y24=z35\frac{x - 1}{5} = \frac{y - 2}{4} = \frac{z - 3}{5} is

A

2x+5y6z=02x + 5y - 6z = 0

B

x+5y5z=0x + 5y - 5z = 0

C

x5y+3z=0x - 5y + 3z = 0

D

x+yz=0x + y - z = 0

Answer

x5y+3z=0x - 5y + 3z = 0

Explanation

Solution

Trick: A general point (5r+1,4r+2,5r+3)( 5 r + 1,4 r + 2,5 r + 3 ) on the line should satisfy the required plane, which is satisfied by x5y+3z=0x - 5 y + 3 z = 0