Skew Lines & Shortest Distance: JEE Questions & Solutions

Let P(,,) be the point on the line x-12 = y+1-3 = z at a distance 4 14 from the point (1,-1,0) and nearer to the origin. Then the shortest…

The sum of all values of, for which the shortest distance between the lines x+1 = y-2-1= z-4- and x = y-12= z-12 is 2, is

Let L1: x-12 = y-23 = z-34 and L2: x-23 = y-44 = z-55 be two lines. Then which of the following points lies on the line of the shortest…

If the square of the shortest distance between the lines x-21 = y-12 = z+3-3 and x+12 = y+34 = z+5-5 is mn, where m and n are co-prime…

The line L1 is parallel to the vector a = -3 i + 2 j + 4 k and passes through the point (7, 6, 2), and the line L2 is parallel to the…

Line L1 passes through the point (1, 2, 3) and is parallel to z-axis. Line L2 passes through the point (, 5, 6) and is parallel to y-axis.…

Let the shortest distance between the lines x-33 = y- -1 = z-31 and x+3-3 = y+72 = z- 4 be 3 30. Then the positive value of 5 + is

Let the values of p, for which the shortest distance between the lines x + 13 = y4 = z5 and r = (p i + 2 j + k) + (2 i + 3 j + 4 k) is 1 6,…

If the shortest distance between the lines x-12 = y-23 = z-34 and x1 = y = z-51 is 5 6, then the sum of all possible values of is:

Let the values of for which the shortest distance between the lines x-12 = y-23 = z-34 and x- 3 = y-44 = z-55 is 1 6 be 1 and 2. Then the…

The shortest distance between the lines x - 41 = y + 12 = z - 31 and x - 2 = y + 14 = z - 2(-5) is 6 5. The sum of all possible values of…

Let O be the origin, and M and N be the points on the lines: x-54 = y-41 = z-53 and x+812 = y+25 = z+119, respectively, such that MN is the…

If d1 is the shortest distance between the lines x+12 = y-1-12 = z1 and x-1-7 = y+82 = z-45, and d2 is the shortest distance between the…

If the shortest distance between the lines x + 62 = y - 64 = z5, x - 3 = y - 2 64 = z + 2 65 is 6, then the square of the sum of all…

The shortest distance between the lines x + 1 = 2y = -12z and x = y + 2 = 6z - 6 is:

If the shortest distance between the line joining the points (1, 2, 3) and (2, 3, 4), and the line x-12 = y+1-1 = z-20 is, then 28 ^2 is…

Shortest distance between the lines x-12 = y+8-7 = z-45 and x-12 = y-21 = z-6-3 is:

The line 1 passes through the point (2, 6, 2) and is perpendicular to the plane 2x + y - 2z = 10. Then the shortest distance between the…

Let the shortest distance between the lines L: x - 52 = y - 0 = z + 11, 0 and L1: x + 1 = y - 1 = 4 - z = 2 6 If (,,) lies on L, then which…

The shortest distance between the lines x-51 = y-22 = z-4-3, x+31 = y+54 = z-1-5 is:

One vertex of a rectangular parallelepiped is at the origin O and the lengths of its edges along x, y and z axes are 3, 4 and 5 units…

The shortest distance between the lines x-44 = y+25 = z+33 and x-13 = y-34 = z-42 is:

The shortest distance between the lines x + 21 = y-2 = z - 52 and x - 41 = y - 12 = z + 30 is:

The distance of the point (-1, 2, 3) from the plane r ( i - 2 j + 3 k) = 10 parallel to the line of the shortest distance between the lines…

The line, that is coplanar to the line x+1-3 = y-21 = z-55, is:

Let S be the set of all values of, for which the shortest distance between the lines x- 0= y-34= z+61 and x+ 3= y-4= z-60 is 13. Then 8 | S…