3D Geometry

JEE Main Mathematics · 17 questions

All 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
• 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 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
• Let the image of the point P(0,-5,0) in the line (x-1)/2=y/1=(z+1)/-2 be the point R and the image of the point Q(0, -1/2, 0) in…20266 April, Shift 2 · Q24
• Let the image of the point P(1,6, a) in the line L: x/1=(y-1)/2=(z-a+1)/b, b>0, be (a/3, 0, a+c). If S(α, β, γ), α>0, is the…20266 April, Shift 1 · Q15
• Let a line L be perpendicular to both the lines L_1: (x+1)/3=(y+3)/5=(z+5)/7 and L_2: (x-2)/1=(y-4)/4=(z-6)/7. If θ is the acute…20266 April, Shift 1 · Q16
• Let a triangle PQR be such that P and Q lie on the line (x+3)/8=(y-4)/2=(z+1)/2 and are at a distance of 6 units from R (1, 2,…20265 April, Shift 2 · Q14
• If the distance of the point (a, 2, 5) from the image of the point (1, 2, 7) in the line x/1=(y-1)/1=(z-2)/2 is 4, then the sum…20265 April, Shift 2 · Q15
• The square of the distance of the point P(5,6,7) from the line (x-2)/2=(y-5)/3=(z-2)/4 is equal to:20265 April, Shift 1 · Q13
• 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
• 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
• If (2 α+1, α^2-3 α, (α-1)/2) is the image of (α, 2 α, 1) in the line (x-2)/3=(y-1)/2=z/1, then the possible value(s) of α is (are)20264 April, Shift 2 · Q14
• 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
• Let the point A be the foot of perpendicular drawn from the point P(a, b, 0) on the line (x-1)/2=(y-2)/1=(z-α)/3. If the midpoint…20262 April, Shift 2 · 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
• Let a line L passing through the point (1,1,1) be perpendicular to both the vectors 2 i+2 j+ k and i+2 j+2 k. If P(a, b, c) is…20262 April, Shift 1 · Q15