If from a point P(a, b, c) perpendiculars PA | vedclass

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

Question

(B) The coordinates of point $P$ are $(a, b, c)$.Since $PA$ is perpendicular to the $yz$-plane,the coordinates of $A$ are $(0, b, c)$.Since $PB$ is pe

Vedclass · Accepted Answer

$bcx + cay - abz = 0$

Vedclass · Answer

(B) The coordinates of point $P$ are $(a, b, c)$.Since $PA$ is perpendicular to the $yz$-plane,the coordinates of $A$ are $(0, b, c)$.Since $PB$ is perpendicular to the $zx$-plane,the coordinates of $B$ are $(a, 0, c)$.The origin $O$ is $(0, 0, 0)$.The equation of a plane passing through the origin is $px + qy + rz = 0$.Since the plane passes through $A(0, b, c)$,we have $p(0) + q(b) + r(c) = 0$,which implies $qb + rc = 0$.Since the plane passes through $B(a, 0, c)$,we have $p(a) + q(0) + r(c) = 0$,which implies $pa + rc = 0$.From these equations,$qb = -rc$ and $pa = -rc$.Thus,$pa = qb = -rc = k$ (where $k$ is a constant).Then $p = k/a$,$q = k/b$,and $r = -k/c$.Substituting these into the plane equation: $(k/a)x + (k/b)y - (k/c)z = 0$.Dividing by $k$ and multiplying by $abc$,we get $bcx + acy - abz = 0$.

If from a point $P(a, b, c)$ perpendiculars $PA$ and $PB$ are drawn to the $yz$-plane and $zx$-plane respectively,then the equation of the plane $OAB$ (where $O$ is the origin) is:

Similar Questions

If a plane is at a distance of $6$ units from the origin and the vector $2 \hat{i} + 6 \hat{j} - 3 \hat{k}$ is its normal,then the equation of the plane in Cartesian form is

If a plane passes through the point $(1, 1, 1)$ and is perpendicular to the line $\frac{x - 1}{3} = \frac{y - 1}{0} = \frac{z - 1}{4}$,then its perpendicular distance from the origin is

The distance of the point $(2, -1, 0)$ from the plane $2x + y + 2z + 8 = 0$ is

Let the plane $x+3y-2z+6=0$ meet the coordinate axes at the points $A, B, C$. If the orthocentre of the triangle $ABC$ is $\left(\alpha, \beta, \frac{6}{7}\right)$,then $98(\alpha+\beta)^2$ is equal to $........$.

The mirror image of the point $(1, 2, 3)$ in a plane is $\left(-\frac{7}{3}, -\frac{4}{3}, -\frac{1}{3}\right)$. Which of the following points lies on this plane?

Vedclass Test Series

Exam Paper Generator

Online Exam Module