Home
Class 11
MATHS
A person standing at the junction (cross...

A person standing at the junction (crossing) of two straight paths represented by the equations `2x + 3y +4 = 0`and `3x + 4y - 5`= 0 wants to reach the path whose equation is `6x - 7y + 8 = 0`in the least time. Find

Text Solution

AI Generated Solution

To solve the problem, we need to find the path that the person should follow to reach the line \(6x - 7y + 8 = 0\) in the least time. This path will be the perpendicular distance from the point of intersection of the two given lines to the third line. ### Step-by-Step Solution: 1. **Find the Point of Intersection (P) of the Two Given Lines:** The equations of the two lines are: \[ 2x + 3y + 4 = 0 \quad \text{(1)} ...
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • STRAIGHT LINES

    NCERT|Exercise EXERCISE 10.1|14 Videos

  • STRAIGHT LINES

    NCERT|Exercise EXERCISE 10.2|20 Videos

  • STRAIGHT LINES

    NCERT|Exercise EXERCISE 10.3|18 Videos

  • STATISTICS

    NCERT|Exercise EXERCISE 15.2|10 Videos

  • TRIGONOMETRIC FUNCTIONS

    NCERT|Exercise EXERCISE 3.1|7 Videos

Similar Questions

Explore conceptually related problems

An elephant standing at the junction of two straight roads represented by the equations x − y+2 = 0 and y − 1 = 0 wants to reach another road whose equation is x − y − 3 = 0 . If the elephant can move in any direction and wants to cover the shortest distance to its destination road, then the equation of the path that the elephant should follow is:

Two straight paths are represented by the equations x - 3y = 2 and -2x + 6y = 5 . Check whether the paths cross each other or not.

Knowledge Check

  • Two straight line paths are represented by the equations 2x -y = 2 and -4x + 2y = 6 . Then , the paths will

    A
    Cross each other at one point
    B
    Not cross each other
    C
    Cross each other at two points
    D
    Cross each other at infinitely many points

  • Two straight line paths are represented by the equation 2x-y=2 and -4x+2y=6 . Then the paths will

    A
    cross each other at one point
    B
    not cross each other
    C
    cross each other at two points
    D
    cross each other at infinitely many points

  • Find the equations of the line through the intersection of 2x - 3y + 4 = 0 and 3x + 4y - 5= 0 and perpendicular to 6x-7y +c = 0

    A
    `119 y + 20 x = 125`
    B
    `199 y - 120 x = 125`
    C
    `119x + 102 y = 125`
    D
    `119 x - 102 y = 125`

    • Similar Questions

    Explore conceptually related problems

    Find the solution of the equations 8x + 5y - 9 = 0 and 3x + 2y - 4 = 0 .

    The system of equations 3x + y -4=0 and 6x + 2y-8=0 has

    Find the distance between 3x + 2y + 7 = 0 and 6x + 4y + 3 = 0.

    Find the equations of the bisectors of the angle between the straight line 3x + 4y + 2 = 0 and 5x - 12y - 6 = 0

    The straight lines 3x - 4y + 7 = 0 and 12x + 5y - 2 = 0 has equation of the acute angle bisector as:

    Home
    Profile