The symmetric equation of the line formed by | vedclass

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

Question

(C) Let $a, b, c$ be the direction ratios of the required line.Since the line lies in both planes,its direction vector is perpendicular to the normals

Vedclass · Accepted Answer

$\frac{x + 1}{-5} = \frac{y - 4}{7} = \frac{z - 0}{1}$

Vedclass · Answer

(C) Let $a, b, c$ be the direction ratios of the required line.Since the line lies in both planes,its direction vector is perpendicular to the normals of both planes,$(3, 2, 1)$ and $(1, 1, -2)$.Thus,$3a + 2b + c = 0$ and $a + b - 2c = 0$.Using cross product,$\frac{a}{(-4 - 1)} = \frac{b}{(1 + 6)} = \frac{c}{(3 - 2)}$,which gives $\frac{a}{-5} = \frac{b}{7} = \frac{c}{1}$.To find a point on the line,set $z = 0$ in the given equations: $3x + 2y = 5$ and $x + y = 3$.Solving these,we get $x = -1$ and $y = 4$.Thus,the point is $(-1, 4, 0)$.The symmetric equation is $\frac{x - (-1)}{-5} = \frac{y - 4}{7} = \frac{z - 0}{1}$,which simplifies to $\frac{x + 1}{-5} = \frac{y - 4}{7} = \frac{z - 0}{1}$.

The symmetric equation of the line formed by the intersection of the planes $3x + 2y + z - 5 = 0$ and $x + y - 2z - 3 = 0$ is:

Similar Questions

The electric current $i$ in the circuit shown is (in $A$)

In which stage does the condensation of chromosomes reach its maximum level?

Which is the major product of the following reaction?

The angle between the asymptotes of the hyperbola $x^2-3y^2=3$ is

Three identical bodies of equal mass $M$ each are moving along a circle of radius $R$ under the action of their mutual gravitational attraction. The speed of each body is

Vedclass Test Series

Exam Paper Generator

Online Exam Module