Skew Lines & Shortest Distance: JEE Questions & Solutions

Let P(α, β, γ) be the point on the line (x-1)/2 = (y+1)/(-3) = z at a distance 4√14 from the point (1,-1,0) and nearer to the origin. Then…

The sum of all values of α, for which the shortest distance between the lines (x+1)/α=(y-2)/(-1)=(z-4)/(-α) and x/α=(y-1)/2=(z-1)/2α is √2,…

Let L₁: (x-1)/2 = (y-2)/3 = (z-3)/4 and L₂: (x-2)/3 = (y-4)/4 = (z-5)/5 be two lines. Then which of the following points lies on the line…

If the square of the shortest distance between the lines (x-2)/1 = (y-1)/2 = (z+3)/(-3) and (x+1)/2 = (y+3)/4 = (z+5)/(-5) is m/n, where m…

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

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

Let the shortest distance between the lines (x-3)/3 = (y-α)/(-1) = (z-3)/1 and (x+3)/(-3) = (y+7)/2 = (z-β)/4 be 3√30. Then the positive…

Let the values of p, for which the shortest distance between the lines (x + 1)/3 = y/4 = z/5 and r = (p i + 2 j + k) + λ (2 i + 3 j + 4 k)…

If the shortest distance between the lines (x-1)/2 = (y-2)/3 = (z-3)/4 and x/1 = y/α = (z-5)/1 is 5/√6, then the sum of all possible values…

Let the values of λ for which the shortest distance between the lines (x-1)/2 = (y-2)/3 = (z-3)/4 and (x-λ)/3 = (y-4)/4 = (z-5)/5 is 1/√6…

The shortest distance between the lines (x - 4)/1 = (y + 1)/2 = z/(-3) and (x - λ)/2 = (y + 1)/4 = (z - 2)/(-5) is 6/√5. The sum of all…

Let O be the origin, and M and N be the points on the lines: (x-5)/4 = (y-4)/1 = (z-5)/3 and (x+8)/12 = (y+2)/5 = (z+11)/9, respectively,…

If d₁ is the shortest distance between the lines x + 1 = 2y = -12z and x = y + 2 = 6z - 6, and d₂ is the shortest distance between the…

If the shortest distance between the lines (x + √6)/2 = (y - √6)/3 = (z - √6)/4 and (x - λ)/3 = (y - 2√6)/4 = (z + 2√6)/5 is 6, then the…

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-1)/2 = (y+1)/(-1) = (z-2)/0 is α,…

Shortest distance between the lines (x-1)/2 = (y+8)/(-7) = (z-4)/5 and (x-1)/2 = (y-2)/1 = (z-6)/(-3) is:

The line ℓ₁ 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 - 5)/2 = (y - λ)/0 = (z + 1)/(-1), λ ≥ 0 and L₁: x + 1 = y - 1 = 4 - z be 2√6. If (α, β,…

The shortest distance between the lines (x-5)/1 = (y-2)/2 = (z-4)/(-3), (x+3)/1 = (y+5)/4 = (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-4)/4 = (y+2)/5 = (z+3)/3 and (x-1)/3 = (y-3)/4 = (z-4)/2 is:

The shortest distance between the lines (x + 2)/1 = y/(-2) = (z - 5)/2 and (x - 4)/1 = (y - 1)/2 = (z + 3)/0 is:

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

The line, that is coplanar to the line (x+3)/(-3) = (y-1)/1 = (z-5)/5, is:

Let S be the set of all values of λ, for which the shortest distance between the lines (x-λ)/0=(y-3)/4=(z+6)/1 and (x+λ)/3=y/(-4)=(z-6)/0…