A plane passes through (2,3,-1) and is perpen | vedclass

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

Question

(D) The equation of a plane passing through the point $(x_1, y_1, z_1)$ with normal vector having direction ratios $(a, b, c)$ is given by $a(x-x_1) +

Vedclass · Accepted Answer

$\frac{13}{\sqrt{74}}$

Vedclass · Answer

(D) The equation of a plane passing through the point $(x_1, y_1, z_1)$ with normal vector having direction ratios $(a, b, c)$ is given by $a(x-x_1) + b(y-y_1) + c(z-z_1) = 0$. Given the point $(2, 3, -1)$,the equation is $a(x-2) + b(y-3) + c(z+1) = 0 \dots (i)$. Since the plane is perpendicular to a line with direction ratios $(3, -4, 7)$,the normal vector of the plane is parallel to this line. Thus,we can take $a=3, b=-4, c=7$. Substituting these into equation $(i)$,we get: $3(x-2) - 4(y-3) + 7(z+1) = 0$ $3x - 6 - 4y + 12 + 7z + 7 = 0$ $3x - 4y + 7z + 13 = 0$. The perpendicular distance $d$ from the origin $(0, 0, 0)$ to the plane $Ax + By + Cz + D = 0$ is given by $d = \frac{|D|}{\sqrt{A^2 + B^2 + C^2}}$. Here,$A=3, B=-4, C=7, D=13$. $d = \frac{|13|}{\sqrt{3^2 + (-4)^2 + 7^2}} = \frac{13}{\sqrt{9 + 16 + 49}} = \frac{13}{\sqrt{74}}$.

$A$ plane passes through $(2,3,-1)$ and is perpendicular to the line having direction ratios $3,-4,7$. The perpendicular distance from the origin to this plane is

Similar Questions

Negation of the statement "The payment will be made if and only if the work is finished in time." is

If the direction ratios of two lines are given by $3lm - 4ln + mn = 0$ and $l + 2m + 3n = 0$,then the angle between the lines is:

Into what does the metacryptoschizont transform through asexual reproduction?

Two seconds after projection,a projectile is travelling in a direction inclined at $30^o$ to the horizontal. After one more second,it is travelling horizontally. What is the magnitude and direction of its velocity at the initial point?

Vedclass Test Series

Exam Paper Generator

Online Exam Module