Line l is r=-8i+5j-6k+t(5i-2k)
Plane is -x-2y+5z = 0
What is the point of intersection? I get (-56/3, 5, -26/15) but my student's school teacher has a different answer of (-23,5,0)
Who is right?
The line is given by x= -8+5t, y= 5, z= -6- 2t.
Putting those into the equation of the plane, -(-8+ 5t)- 2(5)+ 5(-6- 2t)= 8- 5t- 10- 30- 10t= -15t- 32= 0 so that t= -32/15 and then
x= -8+ 5(-32/15)= -8- 32/3= (-24- 32)/3= -56/3.
y= 5
z= -6- 2(-32/15)= (-90+ 64)/15= -26/15