What is the equation of the line passing thro | vedclass

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

Question

(B) The line passes through the point $(x_1, y_1, z_1) = (1, 2, 3)$.Since the line is perpendicular to the plane $3x + 4y - 5z = 6$,the direction vect

Vedclass · Accepted Answer

$\frac{x - 1}{3} = \frac{y - 2}{4} = \frac{3 - z}{5}$

Vedclass · Answer

(B) The line passes through the point $(x_1, y_1, z_1) = (1, 2, 3)$.Since the line is perpendicular to the plane $3x + 4y - 5z = 6$,the direction vector of the line is the same as the normal vector of the plane,$\vec{n} = (3, 4, -5)$.The equation of a line passing through $(x_1, y_1, z_1)$ with direction ratios $(a, b, c)$ is given by $\frac{x - x_1}{a} = \frac{y - y_1}{b} = \frac{z - z_1}{c}$.Substituting the values,we get $\frac{x - 1}{3} = \frac{y - 2}{4} = \frac{z - 3}{-5}$.This can be rewritten as $\frac{x - 1}{3} = \frac{y - 2}{4} = \frac{3 - z}{5}$.

What is the equation of the line passing through $(1, 2, 3)$ and perpendicular to the plane $3x + 4y - 5z = 6$?

Similar Questions

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

The line $\frac{x - 2}{3} = \frac{y - 3}{4} = \frac{z - 4}{5}$ is parallel to which of the following planes?

Let the image of the point $P(2, -1, 3)$ in the plane $x + 2y - z = 0$ be $Q$. Then the distance of the plane $3x + 2y + z + 29 = 0$ from the point $Q$ is $.........$.

Let the line passing through the points $P(2, -1, 2)$ and $Q(5, 3, 4)$ meet the plane $x - y + z = 4$ at the point $R$. Then the distance of the point $R$ from the plane $x + 2y + 3z + 2 = 0$ measured parallel to the line $\frac{x - 7}{2} = \frac{y + 3}{2} = \frac{z - 2}{1}$ is equal to

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

Vedclass Test Series

Exam Paper Generator

Online Exam Module