The co-ordinates of the point where the line \(\displaystyle\frac{x+3}{3}=\frac{y-1}{-1}=\frac{z-5}{-5}\) cuts yz-plane are:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → (0, 0, 0)
Setting each ratio equal to \(\lambda\) gives the general point of the line:
\(\displaystyle \frac{x+3}{3}=\frac{y-1}{-1}=\frac{z-5}{-5} = \lambda\)
\((x, y, z) = (3\lambda - 3,\ 1 - \lambda,\ 5 - 5\lambda)\)
Every point of the yz-plane has x = 0:
\(3\lambda - 3 = 0\), so \(\lambda = 1\)
\((x, y, z) = (0,\ 1 - 1,\ 5 - 5) = (0, 0, 0)\)