Calculus
posted by j on .
7. Where does the line r = (1, 2, 5) + t (2, 3, 1) meet the plane 2x + 5y  3z = 6?

the line can be written as
x = 1 + 2t
y = 2  3t
z = 5 + t
sub that into your plane equation and see if it satisfies the equation 
slightly misread the question.
continue from above
2(1+2t) + 5(23t)  3(5+t) = 6
2 + 4t + 10  15t + 15  3t = 6
14t = 21
t = 21/14 = 3/2
x = 1 + 2(3/2) = 4
y = 2  3(3/2) = 5/2
z = 5 + 3/2 = 7/2
the line intersects at (4, 5/2, 7/2) 
thanks reiny!

welcome