Find the equation of the plane passing throug | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) The general equation of a plane passing through $A(2, 2, -1)$ is given by:$a(x - 2) + b(y - 2) + c(z + 1) = 0 \dots(i)$Since the plane passes thro

Vedclass · Accepted Answer

$5x + 2y - 3z = 17$

Vedclass · Answer

(C) The general equation of a plane passing through $A(2, 2, -1)$ is given by:$a(x - 2) + b(y - 2) + c(z + 1) = 0 \dots(i)$Since the plane passes through $B(3, 4, 2)$ and $C(7, 0, 6)$,we substitute these points into $(i)$:For $B(3, 4, 2)$: $a(3 - 2) + b(4 - 2) + c(2 + 1) = 0 \implies a + 2b + 3c = 0 \dots(ii)$For $C(7, 0, 6)$: $a(7 - 2) + b(0 - 2) + c(6 + 1) = 0 \implies 5a - 2b + 7c = 0 \dots(iii)$Solving $(ii)$ and $(iii)$ using cross-multiplication:$\frac{a}{(2)(7) - (3)(-2)} = \frac{b}{(3)(5) - (1)(7)} = \frac{c}{(1)(-2) - (2)(5)}$$\frac{a}{14 + 6} = \frac{b}{15 - 7} = \frac{c}{-2 - 10}$$\frac{a}{20} = \frac{b}{8} = \frac{c}{-12} \implies \frac{a}{5} = \frac{b}{2} = \frac{c}{-3} = k$Thus,$a = 5k, b = 2k, c = -3k$. Substituting these into $(i)$:$5k(x - 2) + 2k(y - 2) - 3k(z + 1) = 0$$5(x - 2) + 2(y - 2) - 3(z + 1) = 0$$5x - 10 + 2y - 4 - 3z - 3 = 0$$5x + 2y - 3z = 17$.

Find the equation of the plane passing through the points $A(2, 2, -1)$,$B(3, 4, 2)$,and $C(7, 0, 6)$.

Similar Questions

Direction ratios of the normal to a plane passing through $(1, 0, 0)$ and $(0, 1, 0)$ which makes an angle of $\frac{\pi}{4}$ with the plane $x + y - 3 = 0$ are:

If the plane $7x + 11y + 13z = 3003$ meets the coordinate axes at $A, B, C$,then the centroid of the $\triangle ABC$ is

Let $P$ be a plane passing through the points $(2,1,0)$,$(4,1,1)$,and $(5,0,1)$,and $R$ be the point $(2,1,6)$. Then the image of $R$ in the plane $P$ is:

If a plane meets the axes $X, Y, Z$ in $A, B, C$ respectively such that the centroid of $\triangle ABC$ is $(1, 2, 3)$,then the equation of the plane is

The distance of a point $(1, 2, -1)$ from the plane $x - 2y + 4z + 10 = 0$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module