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 line joining the points $A(1,0,0)$ and $B(0,0,1)$ is a normal to the plane $\pi$ which passes through the point $A$, then the angle between the planes $\pi$ and $x+y+z=6$ is

If the three planes $x = 5, 2x - 5ay + 3z - 2 = 0$ and $3bx + y - 3z = 0$ contain a common line,then $(a, b)$ is equal to

The equation of the plane containing the line of intersection of the planes $2x - y = 0$ and $y - 3z = 0$ and perpendicular to the plane $4x + 5y - 3z - 8 = 0$ is

The angle between the line $\frac{x+1}{2}=\frac{y-2}{1}=\frac{z-3}{-2}$ and the plane $x-2y-\lambda z=3$ is $\cos^{-1}\left(\frac{2\sqrt{2}}{3}\right)$. Then the value of $\lambda$ is:

The image of the point $(-1, 3, 4)$ in the plane $x - 2y = 0$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module