Verify please and thank you~
Does the line (x-7)/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.
To verify whether the line and the point determine a plane, you can follow these steps:
1. Start by examining the equation provided: (x-7)/3=(y+8)/6=(z+4)/5.
2. This equation represents a line in three-dimensional space.
3. To determine if the line and the point P(10,-2,1) determine a plane, substitute the coordinates of point P into the equation.
Substitute x=10, y=-2, and z=1 into the equation:
(10-7)/3 = (-2+8)/6 = (1+4)/5
Solving the above equations, we get 3/3 = 6/6 = 5/5, which simplifies to 1 = 1 = 1.
4. If the resulting values from the substitution are equal (as in this case, where we obtained 1 = 1 = 1), then the line and the point lie on the same plane.
Thus, based on the above steps, we can conclude that the line and the point P(10,-2,1) determine a plane.