Three Dimensional Geometry questions
879 published questions with worked solutions.
- Let a line L₁ pass through the origin and be perpendicular to the lines L₂ : r⃗ = (3 + t)î + (2t − 1)ĵ + (2t + 4)k̂ and L₃ : r⃗ =...
- 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...
- The square of the distance of the image of the point (6, 1, 5) in the line (x − 1)/3 = y/2 = (z − 2)/4, from the origin is ______.
- 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 =...
- Let the image of the point (1, 0, 7) in the line x1 = y-1 2 = z-2 3 be the point (α, β, γ). Then which one of the following...
- The lines x-2 2 = y -2 = z-7 16 and x+3 4 = y+2 3 = z+2 1 intersect at the point P. If the distance of P from the line x+1 2 =...
- 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 :
- 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 ΔPQR from the...
- A line with direction ratios 2, 1, 2 meets the lines x = y + 2 = z and x + 2 = 2y = 2z respectively at the points P and Q. If the...
- Let L₁ : r⃗ = (î − ĵ + 2k̂) + λ(î − ĵ + 2k̂), λ ∈ ℝ, L₂ : r⃗ = (ĵ − k̂) + μ(3î + ĵ + pk̂), μ ∈ ℝ, and L₃ : r⃗ = δ(ℓî + mĵ + nk̂),...
- Let a line passing through the point (−1, 2, 3) intersect the lines L₁ : (x − 1)/3 = (y − 2)/2 = (z + 1)/(−2) at M(α, β, γ) and...
- Let (α, β, γ) be the foot of perpendicular from the point (1, 2, 3) on the line x+3 5 = y-1 2 = z+4 3. Then 19(α + β + γ) is...
- Let (α, β, γ) be the mirror image of the point (2, 3, 5) in the line (x − 1)/2 = (y − 2)/3 = (z − 3)/4. Then 2α + 3β + 4γ is...
- Let A(a, b), B(3, 4) and C(−6, −8) respectively denote the centroid, circumcentre and orthocenter of a triangle. Then, the...
- A line passes through A(4, −6, −2) and B(16, −2, 4). The point P(a, b, c), where a, b, c are non-negative integers, on the line...
- Let Q and R be the feet of perpendiculars from the point P(a, a, a) on the lines x = y, z = 1 and x = −y, z = −1 respectively. If...
- Let the acute angle bisector of the two planes x – 2y – 2z + 1 = 0 and 2x – 3y – 6z + 1 = 0 be the plane P. Then which of the...
- If (x, y, z) be an arbitrary point lying on a plane P which passes through the point (42, 0, 0), (0, 42, 0) and (0, 0, 42), then...
- If the distance of the point (1, –2, 3) from the plane x + 2y – 3z + 10 = 0 measured parallel to the line, x-1 3 = 2-y m = z+3 1...
- If for a > 0, the feet of perpendiculars from the points A(a, –2a, 3) and B(0, 4, 5) on the plane x+my+nz=0 are points C(0, –a,...
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