A plane which passes through the point (3, 2, | vedclass

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

Question

(A) The equation of a plane passing through the point $(3, 2, 0)$ is given by $A(x - 3) + B(y - 2) + C(z - 0) = 0 \dots (i)$.Since the plane contains

Vedclass · Accepted Answer

$x - y + z = 1$

Vedclass · Answer

(A) The equation of a plane passing through the point $(3, 2, 0)$ is given by $A(x - 3) + B(y - 2) + C(z - 0) = 0 \dots (i)$.Since the plane contains the line $\frac{x - 3}{1} = \frac{y - 6}{5} = \frac{z - 4}{4}$,it must pass through the point $(3, 6, 4)$ on the line.Substituting $(3, 6, 4)$ into $(i)$,we get $A(3 - 3) + B(6 - 2) + C(4 - 0) = 0$,which simplifies to $4B + 4C = 0$,or $B + C = 0 \dots (ii)$.Also,the normal vector of the plane $(A, B, C)$ must be perpendicular to the direction vector of the line $(1, 5, 4)$. Thus,$1A + 5B + 4C = 0 \dots (iii)$.From $(ii)$,$C = -B$. Substituting into $(iii)$,we get $A + 5B - 4B = 0$,so $A = -B$.Let $B = -1$,then $A = 1$ and $C = 1$.Substituting these into $(i)$,we get $1(x - 3) - 1(y - 2) + 1(z - 0) = 0$,which simplifies to $x - y + z = 1$.

$A$ 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

Similar Questions

If the equation of the plane passing through the point $(2, -1, 3)$ and perpendicular to the planes $3x - 2y + z = 9$ and $x + y + z = 9$ is $x + by + cz + d = 0$,then $d =$

The sine of the angle between the straight line $\frac{x-2}{2}=\frac{y-3}{4}=\frac{4-z}{2}$ and the plane $2x-2y+z=5$ is

If $(\alpha, \beta, \gamma)$ is the intersection point of the lines $x - 3y + 2z + 4 = 0 = 2x + y + 4z + 1$ and $\frac{x - 1/3}{8} = \frac{y}{3} = \frac{z}{-1}$,then $\alpha + \beta + \gamma$ is -

The distance between the line $\frac{x - 1}{3} = \frac{y + 2}{-2} = \frac{z - 1}{2}$ and the plane $2x + 2y - z = 6$ is

The foot of the perpendicular from a point on the circle $x^{2} + y^{2} = 1, z = 0$ to the plane $2x + 3y + z = 6$ lies on which one of the following curves?

Vedclass Test Series

Exam Paper Generator

Online Exam Module