Question

Image of the line $\frac{x-2}{1}=\frac{y-1}{2}=\frac{z}{3}$ in the plane $2x+y+z=5$ is the line-

• A. $\frac{x-2}{-1}=\frac{y-1}{-2}=\frac{z}{15}$
• B. $\frac{x-2}{11}=\frac{1-y}{1}=\frac{z}{-2}$
• C. $\frac{x-2}{11}=\frac{y-1}{1}=\frac{z}{2}$
• D. $\frac{x-2}{11}=\frac{1-y}{1}=\frac{z}{2}$

Answer 1

The correct option is A $\frac{x-2}{-1}=\frac{y-1}{-2}=\frac{z}{15}$

$\begin{array}{c}Bcoordinates\left(2,1,0\right)\\ Acoordinates\left(3,3,3\right)\\ Awillbecalculatedof\\ \frac{x-3}{2}=\frac{y-3}{1}=\frac{2-1}{1}=t\\ \left[2t+3,t+3,t+1\right]\cdot \left[1,2,3\right]=0\\ 2t+32t+6+3t+3=0\\ 7t+12=0\\ t=-\frac{12}{7}\\ A^{\prime }\left[-\frac{3}{7},\frac{9}{7},\frac{-5}{7}\right]\\ Willbe\\ \frac{x-2}{-1}=\frac{y-1}{-2}=\frac{z}{15}\end{array}$