Question

Найти точку M0 пересечения прямой, проходящей через точки M1 = (4, 3, 0), M2 = (1, 2, 5), и плоскости 7x + 3y + 5z-5 = 0

Answer 1

$M_1(4,3,0)\; ,\; \; M_2(1,2,5)\\\\\pi :\; \; 7x+3y+5z-5=0\\\\M_1M_2:\; \; \frac{x-4}{-3}=\frac{y-3}{-1}=\frac{z}{5}\; \; \Rightarrow \; \; \frac{x-4}{3}=\frac{y-3}{1}=\frac{z}{-5}\; \; \Rightarrow \\\\M_1M_2:\; \; \left\{\begin{array}{c}x=3t+4\\y=t+3\\z=-5t\end{array}\right \\\\\\M_1M_2\cap \pi =M_0\\\\7(3t+4)+3(t+3)+5(-5t)-5=0\\\\21t+28+3t+9-25t-5=0\\\\32-t=0\; ,\; \; \underline {t=32}\\\\\left\{\begin{array}{ccc}x=3\cdot 32+4=100\\y=32+3=35\\z=-5\cdot 32=-160\end{array}\right \; \; \Rightarrow \; \; M_0(100,35,-160)$