Shortest Distance between Two Lines

IMPORTANT

Shortest Distance between Two Lines: Overview

This topic covers concepts, such as, Shortest Distance between Two Skew Lines in Vector Form, Distance between Two Parallel Lines in 3D & Shortest Distance between Two Skew Lines etc.

Important Questions on Shortest Distance between Two Lines

HARD
IMPORTANT

Find the distance of the point  1, 5, 10, from the point of intersection of the line r=2i^j^+2k^+λ3i^+4j^+2k^ and the plane ri^j^+k^=5.

EASY
IMPORTANT

The shortest distance between the lines  :

  r =(1t) i ^ +(t2) j ^ +(32t) k ^ and r =(s+1) i ^ +(2s1) j ^ (2s+1) k ^ is

HARD
IMPORTANT

The shortest distance between the following lines is

r=(1+λ)i^+(2λ)j^+(λ+1)k^;

r=(2i^j^k^)+μ(2i^+j^+2k^)         

HARD
IMPORTANT

The distance of the point (–2, 3, –4) from the line   x+2 3 = 2y+3 4 = 3z+4 5  measured parallel to the plane   4x+12y3z+1=0 would be :

HARD
IMPORTANT

The shortest distance between the following two lines:

 r=(i^+2j^+3k^)+λ(i3j^+2k^);

r=4+2μi^+5+3μj^+6+μk^.

HARD
IMPORTANT

What would be the shortest distance between the lines  l1 and l2 whose vector equations are   r = i ^ + j ^ +λ(2 i ^ j ^ + k ^ )  and   r =2 i ^ + j ^ k ^ +μ(3 i ^ 5 j ^ +2 k ^ ) ?

HARD
IMPORTANT

What would be the shortest distance between the lines  l1 and l2 whose vector equations are   r = i ^ + j ^ +λ(2 i ^ j ^ + k ^ )  and   r =2 i ^ + j ^ k ^ +μ(3 i ^ 5 j ^ +2 k ^ ) ?

HARD
IMPORTANT

Find the shortest distance between the lines r=3i^+2j^-4k^+λ(i^+2j^+2k^) and r=5i^-2j^+μ(3i^+2j^+6k^).

If the lines intersect find their point of intersection.

HARD
IMPORTANT

The shortest distances between the diagonals of a rectangular parallelepiped whose sides are a, b, c and the edges not meeting it are bcb2+c2,cac2+a2,aba2+b2.

HARD
IMPORTANT

Shortest distance between the following pair of lines r=(i^+2j^+k^)+λ(i^-j^+k^) and r=(2i^-j^-k^)+μ(2i^+j^+2k^) is

MEDIUM
IMPORTANT

The following pairs of lines r=(i^-j^)+λ(2i^+k^) and r=(2i^-j^)+μ(i^+j^-k^) are intersecting lines.

HARD
IMPORTANT

If the shortest distance between the lines r=(4i^-j^)+λ(i^+2j^-3k^) and r=(i^-j^+2k^)+μ(i^+4j^-5k^) is 1m, then the value of m is

MEDIUM
IMPORTANT

If the shortest distance between the lines
r=(4i^-j^)+λ(i^+2j^-3k^)  and r=(i^-j^+2k^)+μ(2i^+4j^-5k^) is a5, then a=
 

HARD
IMPORTANT

Find the shortest distance between the pair of lines:

r=i^+2j^-4k^+λ(2i^+3j^+6k^) and r=3i^+3j^-5k^+μ(2i^+3j^+6k^)

HARD
IMPORTANT

Find the shortest distance between the pair of lines:

x-32=y-41=z+1-3 and  x-1-1=y-33=z-12

HARD
IMPORTANT

By computing the shortest distance determine whether the following lines intersect or not: x-54=y-7-5=z+3-5 and x-87=y-71=z-53.

HARD
IMPORTANT

By computing the shortest distance determine whether the following pairs of lines intersect or not: r=(i^-j^)+λ(2i^+k^) and r=(2i^-j^)+μ(i^+j^-k^).

HARD
IMPORTANT

By computing the shortest distance, determine whether the lines r¯=(i^-j^)+λ(2i^+k^) and r¯=2i^-j^+μ(i^-j^+k^)  intersect or not.

HARD
IMPORTANT

If the lines x-12=y+13=z-14 and x-31=y-k2=z1 intersect, then find the value of k.

HARD
IMPORTANT

If the shortest distance between the lines r=(λ-1)i^+(λ+1)j^-(1+λ)k^ and r=(1-μ)i^+(2μ-1)j^+(μ+2)k^ is of the form of a2, then a=