Home
Class 12
MATHS
Find the distance of point (2, 0, 1) fro...

Find the distance of point (2, 0, 1) from the line whose symmetric equations are
`(x-2)/3=(y+1)/4=(z-1)/(-2)`.

Text Solution

Verified by Experts

Distance of line from a given point
`=abs((vec(PA)xx(ahati+bhatj+chatk))/(abs(ahati+bhatj+chatk)))`
here `vec(PA)=hatj`
`ahati+ bhatj +c hatk =3hati + 4hatj-2hatk`
so distance will be
`=abs((hatj xx (3hati +4hatj-2hatk))/(sqrt(9+16+4)))`
`=abs((-3hatk-2hati)/(sqrt(29)))= sqrt(13/29)`
Promotional Banner

Topper's Solved these Questions

  • THREE DIMENSIONAL GEOMETRY

    AAKASH INSTITUTE|Exercise Illustration|4 Videos

  • THREE DIMENSIONAL GEOMETRY

    AAKASH INSTITUTE|Exercise TRY YOURSELF|97 Videos

  • STRAIGHT LINES

    AAKASH INSTITUTE|Exercise SECTION-J (AAKASH CHALLENGERS QUESTIONS)|5 Videos

  • TRIGNOMETRIC FUNCTIONS

    AAKASH INSTITUTE|Exercise Section - J (Akash Challengers Question)|15 Videos

Similar Questions

Explore conceptually related problems

Find the distance of the point (2, 0, 4) from the plane whose equation is x + y - 2z =0.

Find the equation ot the plane through the point p(5, 3, -1) perpendicular to the line in space whose symmetric equations are (x-2)/3=(y+1)/4=(z-1)/-2 . (Vector form)

Find the distance of the point (-1,-5,-10) from the point of intersection of the line (x-2)/(3)=(y+1)/(4)=(z-2)/(12) and plane x-y+z=5 .

Find the distance of the point (1,2,0) from the plane 4x+3y+12z+16=0

Find the distance of the point (-2, 3, -5) from the line (x+2)/1=(y-3)/2=z/3.

Find the distance of the point (1, 2-1) from the plane x -2y + 4z - 10 = 0 .

Find the distance from the point (3,4,5) to the point, where the line: (x - 3)/(1) = (y - 4)/(2) = (z - 5)/(2) meets the plane x + y + z = 2.

Statement 1: A point on the line (x+2)/3=(y+1)/2=(z-3)/2 at a distance 3sqrt(2) from the point (1,2,3) lies on the lne (x+7)/5=(y+t)/4=(z-2)/1 Statement 2: If d is the distance between the point (-1,-5,-10) and the point of intersectionof the line (x-2)/3=(y+1)/4=(z-2)/12 with the plane x-y+z=5 then d=13

Find the distance of the point (0.-3.-2) from the plane x+2y-z=1 measured parallel to (x+1)/(2)=(y+1)/(2)=(z)/(3)