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Class 12 Chapter Maths
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12 Ch. 11 Maths
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The Three Dimensions of Greta 1971
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12th
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Chapter 12
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Chapter 3D Geometry
Class 11 Maths
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Q) Determine if the line 𝑟 =(𝑖 +𝑗 −𝑘 )+𝜆(3𝑖 −𝑗 ) and 𝑟 =(4𝑖 −𝑘 )+𝜇(2𝑖 ˆ+3𝑘 ˆ) interse
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Q) Find the image A^′ of the point A(1,6,3) in the line 𝑥/1=(y−1)/2=(z−2)/3. Also, find the
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Q) Find the equation of a line in vector and cartesian form which passes through the point ( 1,2,−4
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Q) Find the foot of the perpendiculardrawn from the point (1,1,4) of the line (x+2)/5 = (y+1)/2
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Q) The line x=1+5μ , 𝑦=−5+ 𝜇, 𝑧=−6− 3𝜇 𝑝𝑎𝑠𝑠𝑒𝑠 𝑡ℎrough which of the following point ?
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Q) Find the coordinates of the foot of the perpendicular and the length of the perpendicular drawn
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Q) The equation of a line parallel to the vector 3𝑖+𝑗 +2𝑘 and passing through the point (4,−3,7)
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Q) Find the point on the line (𝑥−1)/3=(𝑦+1)/2=(𝑧−4)/3 at a distance of 2√2 units from the point
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Q) If a line makes angles of 3𝜋/4,𝜋/3 and 𝜃 with the positive directions of 𝑥,𝑦 and z -axis
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Q) Find the image A^′ of the point A(2,1,2) in the line 𝑙:r =4i +2j +2k +𝜆(i −j −k ). Also, find
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Q) Find the image A^′ of the point A(1,6,3) in the line 𝑥/1=(y−1)/2=(z−2)/3. Also, find the
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Q) Find the shortest distance between the lines given by(𝑟 =(4𝑖 −𝑗 +2𝑘 )+𝜆(𝑖 +2𝑗 −3𝑘 )
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Q) Find the angle between the two lines whose equations are 2𝑥=3𝑦=−𝑧 and 6𝑥=−𝑦=−4𝑧.
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Q) The coordinates of the foot of the perpendicular drawn from the point A(−2,3,5) on the y -axis
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Shivang Gupta on Instagram: "Cbse pyq 2025 three dimensional geometry class 12 class 12 Q) Find the value of 𝜆 if the following lines are perpendicular to each other : 𝑙_1:(1−x)/(−3)=(3y−2)/2𝜆=(z−3)/3𝑙_2:(x−1)/3𝜆=(1−y)/1=(2z−5)/3) Cbse pyq 2025 three dimensional geometry class 12 class 12 : class 12 physics chapter 12 ncert solutions : class 12 maths chapter 11 all formulas : class 9 maths chapter 11 ncert solutions : class 12 maths chapter 11 introduction : class 12 maths chapter 5 ncert s
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Q) Find the shortest distance between the lines:(𝑥+1)/2=(𝑦−1)/1=(𝑧−9)/(−3) " and (𝑥−3)/2=(𝑦+15)/(−7
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