Shortest distance between two lines

JEE Main Mathematics · 3D Geometry · 38 questions, latest first

• Let the foot of perpendicular from the point (λ, 2,3) on the line (x-4)/1=(y-9)/2=(z-5)/1 be the point (1, μ, 2). Then the…20268 April, Shift 2 · Q15
• The shortest distance between the lines (x-4)/1=(y-3)/2=(z-2)/-3 and (x+2)/2=(y-6)/4=(z-5)/-5 is:20266 April, Shift 2 · Q14
• The shortest distance between the lines r=(1/3 i+2 j+8/3 k)+λ(2 i-5 j+6 k) and r=(-2/3 i-1/3 k)+μ( j- k), λ, μ ∈ R, is:20264 April, Shift 2 · Q13
• 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…202624 January, Shift 2 · Q13
• 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.…202622 January, Shift 1 · Q14
• 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…20258 April, Shift 2 · Q15
• 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…20257 April, Shift 1 · Q14
• 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) is…20254 April, Shift 2 · Q14
• 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…20254 April, Shift 1 · Q14
• Line L_1 passes through the point (1,2,3) and is parallel to z -axis. Line L_2 passes through the point (λ, 5,6) and is parallel…20253 April, Shift 1 · Q14
• The line L_1 is parallel to the vector a=-3 i+2 j+4 k and passes through the point (7,6,2) and the line L_2 is parallel to the…20252 April, Shift 2 · Q15
• 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, n…202523 January, Shift 2 · Q13
• Let L_1: (x-1)/2=(y-2)/3=(z-3)/4 and L_2: (x-2)/3=(y-4)/4=(z-5)/5 be two lines. Then which of the following points lies on the…202522 January, Shift 1 · Q15
• The shortest distance between the lines (x-3)/4=(y+7)/-11=(z-1)/5 and (x-5)/3=(y-9)/-6=(z+2)/1 is:20249 April, Shift 1 · Q16
• If the shortest distance between the lines (x-λ)/2=(y-4)/3=(z-3)/4 and (x-2)/4=(y-4)/6=(z-7)/8 is 13/(√29), then a value of λ is:20248 April, Shift 2 · Q16
• If the shortest distance between the lines L_1: r=(2+λ) i+(1-3 λ) j+(3+4 λ) k, λ ∈ R; L_2: r=2(1+μ) i+3(1+μ) j+(5+μ) k, μ ∈ R is…20248 April, Shift 1 · Q14
• If the shortest distance between the lines (x-λ)/3=(y-2)/-1=(z-1)/1 and (x+2)/-3=(y+5)/2=(z-4)/4 is 44/(√30), then the largest…20246 April, Shift 2 · Q28
• The shortest distance between the lines (x-3)/2=(y+15)/-7=(z-9)/5 and (x+1)/2=(y-1)/1=(z-9)/-3 is20246 April, Shift 1 · Q17
• Let the point (-1, α, β) lie on the line of the shortest distance between the lines (x+2)/-3=(y-2)/4=(z-5)/2 and…20245 April, Shift 2 · Q28
• If the shortest distance between the lines (x+2)/2=(y+3)/3=(z-5)/4 and (x-3)/1=(y-2)/-3=(z+4)/2 is 38/(3 √5) k, and ∫_0^k[x^2] d…20244 April, Shift 1 · Q29
• If the shortest distance between the lines (x-λ)/-2=(y-2)/1=(z-1)/1 and (x-√3)/1=(y-1)/-2=(z-2)/1 is 1, then the sum of all…20241 February, Shift 1 · Q16
• Let the line of the shortest distance between the lines L_1: r=( i+2 j+3 k)+λ( i- j+ k) and L_2: r=(4 i+5 j+6 k)+μ( i+ j- k)…20241 February, Shift 1 · Q30
• The shortest distance, between lines L_1 and L_2, where L_1: (x-1)/2=(y+1)/-3=(z+4)/2 and L_2 is the line, passing through the…202431 January, Shift 2 · Q17
• If d_1 is the shortest distance between the lines x+1=2 y=-12 z, x=y+2=6 z-6 and d_2 is the shortest distance between the lines…202430 January, Shift 1 · Q28
• 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…202429 January, Shift 2 · Q30
• If 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), then the sum of all…202427 January, Shift 1 · Q18
• 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…202315 April, Shift 1 · Q15
• The shortest distance between the lines (x+2)/1=y/-2=(z-5)/2 and (x-4)/1=(y-1)/2=(z+3)/0 is202310 April, Shift 1 · Q15
• 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 is20238 April, Shift 1 · Q16
• One vertex of a rectangular parallelopiped is at the origin O and the lengths of its edges along x, y and z axes are 3, 4 and 5…20236 April, Shift 1 · Q14
• The shortest distance between the lines (x-5)/1=(y-2)/2=(z-4)/-3 and (x+3)/1=(y+5)/4=(z-1)/-5 is20231 February, Shift 1 · Q76
• Let the shortest distance between the lines L: (x-5)/-2=(y-λ)/0=(z+λ)/1, λ ≥ 0 and L_1: x+1=y-1=4-z be 2 √6. If (α, β, γ) lies on…202331 January, Shift 1 · Q76
• The line l_1 passes through the point (2,6,2) and is perpendicular to the plane 2 x+y-2 z=10. Then the shortest distance between…202330 January, Shift 1 · Q75
• The shortest distance between the lines (x-1)/2=(y+8)/-7=(z-4)/5 and (x-1)/2=(y-2)/1=(z-6)/-3 is202329 January, Shift 2 · Q73
• The shortest distance between the lines x+1=2 y=-12 z and x=y+2=6 z-6 is202325 January, Shift 2 · Q75
• 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,…202325 January, Shift 2 · Q88
• If the shortest 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 square of sum of…202324 January, Shift 2 · Q90
• The shortest distance between the lines (x-2)/3=(y+1)/2=(z-6)/2 and (x-6)/3=(1-y)/2=(z+8)/0 is equal to ____202324 January, Shift 1 · Q90