The co-ordinates of the point at which the line \(\displaystyle\frac{x-3}{3}=\frac{y+1}{2}=\frac{z-4}{-2}\) crosses \(xy\) plane, are
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → (9, 3, 0)
Let each ratio equal \(\lambda\). A general point of the line is
\((3\lambda + 3,\ 2\lambda - 1,\ -2\lambda + 4)\)
On the xy-plane, z = 0:
\(-2\lambda + 4 = 0,\quad \lambda = 2\)
\(x = 3(2) + 3 = 9,\quad y = 2(2) - 1 = 3\)
So the line crosses the xy-plane at (9, 3, 0).