The equation of the straight line passing thr | vedclass

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

Question

(A) The equation of a line passing through the point $(x_1, y_1, z_1)$ with direction ratios $(a, b, c)$ is given by $\frac{x - x_1}{a} = \frac{y - y_

Vedclass · Accepted Answer

$\frac{x - 1}{1} = \frac{y - 2}{2} = \frac{z - 3}{-5}$

Vedclass · Answer

(A) The equation of a line passing through the point $(x_1, y_1, z_1)$ with direction ratios $(a, b, c)$ is given by $\frac{x - x_1}{a} = \frac{y - y_1}{b} = \frac{z - z_1}{c}$.The given point is $(1, 2, 3)$,so the equation is $\frac{x - 1}{a} = \frac{y - 2}{b} = \frac{z - 3}{c}$.$A$ line is perpendicular to a plane if its direction ratios are proportional to the normal vector of the plane.The equation of the plane is $x + 2y - 5z + 9 = 0$,so the normal vector is $\vec{n} = (1, 2, -5)$.Thus,the direction ratios of the line are $(1, 2, -5)$.Substituting these into the line equation,we get $\frac{x - 1}{1} = \frac{y - 2}{2} = \frac{z - 3}{-5}$.

The equation of the straight line passing through $(1, 2, 3)$ and perpendicular to the plane $x + 2y - 5z + 9 = 0$ is

Similar Questions

The equation of the plane that contains the line of intersection of the planes $x+2y+3z-4=0$ and $2x+y-z+5=0$ and is perpendicular to the plane $5x+3y-6z+8=0$ is

If the line $\frac{x - 3}{1} = \frac{y + 2}{-1} = \frac{z + \lambda}{-2}$ lies in the plane $2x - 4y + 3z = 2$,then the shortest distance between this line and the line $\frac{x - 1}{12} = \frac{y}{9} = \frac{z}{4}$ is

Find the equation of the plane containing the line $\frac{x + 1}{-3} = \frac{y - 3}{2} = \frac{z + 2}{1}$ and the point $(0, 7, -7)$.

Let the plane $P$ contain the line $2x+y-z-3=0=5x-3y+4z+9$ and be parallel to the line $\frac{x+2}{2}=\frac{3-y}{-4}=\frac{z-7}{5}$. Then the distance of the point $A(8,-1,-19)$ from the plane $P$ measured parallel to the line $\frac{x}{-3}=\frac{y-5}{4}=\frac{2-z}{-12}$ is equal to $............$.

Find the point of intersection of the line $\frac{x}{1} = \frac{y}{2} = \frac{z}{2}$ and the plane $2x + y + z = 6$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module