Practicing Success
A plane which passes through the point (3, 2, 0) and the line $\frac{x-3}{1}=\frac{y-6}{5}=\frac{z-4}{4}$, is |
$x- y + z = 1 $ $x+ y + z = 5 $ $x+2 y - z = 1 $ $2x- y + z = 5 $ |
$x- y + z = 1 $ |
The equation of a plane containing the line $\frac{x-3}{1}=\frac{y-6}{5}=\frac{z-4}{4}$ is $a(x-3) + b(y-6) + c(z-4) = 0 $ .....(i) where, $a + 5b + 4c = 0 $ ..........(ii) This plane will pass through (3, 2, 0) if $a(0)+ b(-4) + c(-4) = 0 $ .........(iii) Solving (i) and (iii), we get $\frac{a}{-20+16}=\frac{b}{0+4} = \frac{c}{-4+0}⇒ \frac{a}{1}=\frac{b}{-1}=\frac{c}{1}$ Putting the values of a, b, c in (i), we obtain that the equation of the planes is x - y + z -1 = 0. |