Posted by Antia on Monday, April 9, 2012 at 8:22pm.
Verify please and thank you~
1. Does the line (x7)/3=(y+8)/6=(z+4)/5 and the point P(10,2,1) determine a plane?
Answer: Yes, it is a plane because when I substituted the point P(10,2,1) into the equation, I got the coordinates (1,1,1) If the coordinate became to be (0,0,0) then it wouldn't be a plane.

Calculus and vectors  MathMate, Monday, April 9, 2012 at 11:18pm
L1: (x7)/3=(y+8)/6=(z+4)/5
When P(10,2,1) is substituted into L1, we get 1=1=1 which means that P is on the line.
To define a plane from a point and a line, the point must NOT lie on the line else the plane is undefined.
So the answer is no, because the point P lies on the given line.