Coplanarity and intersection of lines

JEE Main Mathematics · 3D Geometry · 32 questions, latest first

• Let a line L_1 pass through the origin and be perpendicular to the lines L_2: r=(3+t) i+(2 t-1) j+(2 t+4) k and L_3: r=(3+2 s)…20268 April, Shift 2 · Q23
• The square of the distance of the point of intersection of the lines r=( i+ j- k)+λ(a i- j), a ≠ 0 and r=(4 i- k)+μ(2 i+a k) from…20265 April, Shift 1 · Q15
• A line with direction ratios 1,-1,2 intersects the lines x/2=y/3=(z+1)/3 and (x+1)/-1=(y-2)/1=z/4 at the points P and Q,…20264 April, Shift 1 · Q14
• The square of the distance of the point (-2,-8,6) from the line (x-1)/1=(y-1)/2=z/-1 along the line (x+5)/1=(y+5)/-1=z/2 is equal…20264 April, Shift 1 · Q15
• If the point of intersection of the lines (x+1)/3=(y+a)/5=(z+b+1)/7 and (x-2)/1=(y-b)/4=(z-2 a)/7 lies on x y -plane, then the…20262 April, Shift 1 · Q13
• If the distance of the point P(43, α, β), β<0, from the line r=4 i- k+μ(2 i+3 k), μ ∈ R along a line with direction ratios 3, -1,…202628 January, Shift 2 · Q24
• If the distances of the point (1,2, a) from the line (x-1)/1=y/2=(z-1)/1 along the lines L_1: (x-1)/3=(y-2)/4=(z-a)/b and L_2:…202628 January, Shift 1 · Q13
• Let the lines L_1: r= i+2 j+3 k+λ(2 i+3 j+4 k), λ ∈ R and L_2: r=(4 i+ j)+μ(5 i+2 j+ k), μ ∈ R, intersect at the point R. Let P…202624 January, Shift 1 · Q16
• Let L be the line (x+1)/2=(y+1)/3=(z+3)/6 and let S be the set of all points (a, b, c) on L, whose distance from the line…202622 January, Shift 2 · Q15
• Let the line L_1 be parallel to the vector -3 i+2 j+4 k and pass through the point ( 2,6,7 ), and the line L_2 be parallel to the…202621 January, Shift 2 · Q15
• Let the area of the triangle formed by the lines x+2=y-1=z, (x-3)/5=y/-1=(z-1)/1 and x/-3=(y-3)/3=(z-2)/1 be A. Then A^2 is equal…20258 April, Shift 2 · Q24
• Let the line L pass through (1,1,1) and intersect the lines (x-1)/2=(y+1)/3=(z-1)/4 and (x-3)/1=(y-4)/2=z/1. Then, which of the…20257 April, Shift 1 · Q13
• The distance of the point (7,10,11) from the line (x-4)/1=(y-4)/0=(z-2)/3 along the line (x-9)/2=(y-13)/3=(z-17)/6 is20253 April, Shift 2 · Q15
• Let a line passing through the point (4,1,0) intersect the line L_1: (x-1)/2=(y-2)/3=(z-3)/4 at the point A(α, β, γ) and the line…20253 April, Shift 1 · Q15
• Let L_1: (x-1)/1=(y-2)/-1=(z-1)/2 and L_2: (x+1)/-1=(y-2)/2=z/1 be two lines. Let L_3 be a line passing through the point (α, β,…202529 January, Shift 1 · Q14
• Let a= i+2 j+ k and b=2 i+7 j+3 k. Let L_1: r=(- i+2 j+ k)+λ a, λ ∈ R and L_2: r=( j+ k)+μ b, μ ∈ R be two lines. If the line L_3…202529 January, Shift 1 · Q15
• The square of the distance of the point (15/7, 32/7, 7) from the line (x+1)/3=(y+3)/5=(z+5)/7 in the direction of the vector i+4…202528 January, Shift 2 · Q16
• Let the line passing through the points (-1,2,1) and parallel to the line (x-1)/2=(y+1)/3=z/4 intersect the line…202524 January, Shift 1 · Q15
• The distance of the line (x-2)/2=(y-6)/3=(z-3)/4 from the point (1,4,0) along the line x/1=(y-2)/2=(z+3)/3 is:202523 January, Shift 2 · Q12
• Consider the line L passing through the points (1,2,3) and (2,3,5). The distance of the point (11/3, 11/3, 19/3) from the line L…20249 April, Shift 2 · Q16
• Let the line L intersect the lines x-2=-y=z-1,2(x+1)=2(y-1)=z+1 and be parallel to the line (x-2)/3=(y-1)/1=(z-2)/2. Then which…20249 April, Shift 1 · Q15
• Let d be the distance of the point of intersection of the lines (x+6)/3=y/2=(z+1)/1 and (x-7)/4=(y-9)/3=(z-4)/2 from the point…20245 April, Shift 1 · Q17
• Let a line passing through the point (-1,2,3) intersect the lines L_1: (x-1)/3=(y-2)/2=(z+1)/-2 at M(α, β, γ) and L_2:…202430 January, Shift 2 · Q29
• Let PQR be a triangle with R(-1,4,2). Suppose M(2,1,2) is the mid point of PQ. The distance of the centroid of PQR from the point…202429 January, Shift 1 · Q16
• A line with direction ratios 2, 1, 2 meets the lines x=y+2=z and x+2=2 y=2 z respectively at the points P and Q. If the length of…202429 January, Shift 1 · Q29
• The distance, of the point (7,-2,11) from the line (x-6)/1=(y-4)/0=(z-8)/3 along the line (x-5)/2=(y-1)/-3=(z-5)/6, is:202427 January, Shift 1 · Q17
• The line, that is coplanar to the line (x+3)/-3=(y-1)/1=(z-5)/5, is202313 April, Shift 2 · Q15
• Let the lines l_1: (x+5)/3=(y+4)/1=(z-α)/-2 and l_2: 3 x+2 y+z-2=0=x-3 y+2 z-13 be coplanar. If the point P(a, b, c) on l_1 is…202312 April, Shift 1 · Q15
• Let the line x/1=(6-y)/2=(z+8)/5 intersect the lines (x-5)/4=(y-7)/3=(z+2)/1 and (x+3)/6=(3-y)/3=(z-6)/1 at the points A and B…202310 April, Shift 2 · Q15
• If the lines (x-1)/2=(2-y)/-3=(z-3)/(α) and (x-4)/5=(y-1)/2=z/(β) intersect, then the magnitude of the minimum value of 8 α β is…20236 April, Shift 2 · Q28
• If the lines (x-1)/1=(y-2)/2=(z+3)/1 and (x-a)/2=(y+2)/3=(z-3)/1 intersect at the point P, then the distance of the point P from…202329 January, Shift 2 · Q74
• Consider the lines L_1 and L_2 given by L_1: (x-1)/2=(y-3)/1=(z-2)/2; L_2: (x-2)/1=(y-2)/2=(z-3)/3. A line L_3 having direction…202325 January, Shift 1 · Q66