Three Dimensional Geometry

36 solved questions from Class 12 Mathematics, each with the full working. Tap any question to see the step-by-step solution.

• 1 What is the domain, range, or fundamental theorem introduced in 'Three Dimensional Geometry' (Class 12 Mathematics)? medium MCQ Functions & Theorems
• 2 What is the derivative or integral formula associated with 'Three Dimensional Geometry'? medium MCQ Calculus & Formulae
• 3 How do you find the solution set or optimum value in 'Three Dimensional Geometry'? medium MCQ Problem Solving & Optimization
• 4 Which of the following is the equation of the plane that passes through the point (1,2,3) and has normal vector ⟨ 4,-1,2⟩? easy MCQ 1 mark Plane through point with given normal
• 5 Find the perpendicular distance from the point P(1,2,3) to the plane 2x - y + 2z = 7. medium 3 marks Distance of point from a plane
• 6 Find the equation of the plane that passes through the point (2,-1,4) and has normal vector ⟨ 3,-2,5⟩. easy MCQ 2 marks Equation of a plane
• 7 The line L is given by the parametric equations x = 1 + 2t, y = -1 + t, z = 3 - t. Find the acute angle between this line and the plane 4x + y - 2z + 5 = 0. Give your answer in degrees rounded to the nearest integer. medium 3 marks Angle between line and plane
• 8 Find the shortest distance between the two skew lines L_1:(x-1)/2 = (y+1)/-1 = (z-3)/3 and L_2:(x+2)/1 = (y-4)/2 = (z+1)/-2. hard 5 marks Shortest distance between skew lines
• 9 Find the shortest distance between the skew lines L_1:; x=1+3t,; y=-2+2t,; z=5+t and L_2:; (x-4)/2=(y+3)/-1=(z-1)/4. hard 5 marks Shortest distance between skew lines
• 10 Calculate the perpendicular distance from the point Q(4,-2,1) to the plane 3x+2y-5z=12. medium 3 marks Distance from point to plane
• 11 The angle between the planes x-2y+3z=4 and 2x+y-z=0 is closest to which of the following values?\n(a) 50^circ\n(b) 70^circ\n(c) 71^circ\n(d) 80^circ medium MCQ 3 marks Angle between two planes
• 12 Find the equation of the plane that passes through the points (0,1,2), (2,-1,1), and (1,3,0). easy 2 marks Plane through three points
• 13 Find the equation of the plane that passes through the point ((3,,-2,,1)) and is parallel to the plane (2x-y+3z=4). easy 1 mark Equation of a plane parallel to a given plane
• 14 Find the shortest distance between the skew lines (displaystyle \frac{x-2}{4}=\frac{y+1}{-3}=\frac{z-5}{2}) and (displaystyle \frac{x-0}{1}=\frac{y-4}{2}=\frac{z+1}{-1}). hard 5 marks Shortest distance between skew lines
• 15 A plane passes through the points ((1,0,2),;(2,3,0),;(4,-1,1)). Compute the perpendicular distance from the point ((5,-1,2)) to this plane. hard 4 marks Distance from point to a plane
• 16 Find the shortest distance between the skew lines L_1: (x-2)/1=(y+3)/2=(z-1)/-1 and L_2: (x+1)/3=(y-4)/-1=(z+2)/2. hard 4 marks Shortest distance between skew lines
• 17 Find the equation of the plane that passes through the point (1,2,3) and is parallel to the plane 2x-3y+z=5. easy 1 mark Plane equation from point and normal vector
• 18 Find the perpendicular distance from the point P(4,-1,2) to the plane 3x+4y-2z=12. medium 2 marks Distance from point to plane
• 19 Find the acute angle between the line x=5+3t, y=-2+4t, z=1-2t and the plane 2x - y + 3z = 7. hard MCQ 4 marks Angle between line and plane
• 20 Write the equation of the plane that passes through the point (2,,-1,,4) and is parallel to the plane 4x-y+2z=7. medium 3 marks Plane through point parallel to given plane
• 21 Find the shortest distance between the skew lines L_1:(x-1)/2=(y+2)/-3=(z-5)/1 and L_2:(x+3)/1=(y-4)/2=(z-2)/-2. hard 5 marks Shortest distance between skew lines
• 22 Find the perpendicular distance of the point P(3,,-2,,5) from the plane 2x+3y-z=10. easy 2 marks Distance from point to plane
• 23 Find the perpendicular distance of the point P(2,-3,6) from the plane 3x-4y+12z=30. easy 2 marks Distance of a point from a plane
• 24 Find the equation of the plane that passes through the point (1,-2,3) and is parallel to the plane 5x-y+2z=7. medium MCQ 3 marks Plane parallel to a given plane
• 25 Find the shortest distance between the skew lines L_1: (x-1)/2=(y+2)/-1=(z-3)/4 and L_2: (x+3)/-3=(y-1)/2=(z+2)/1. hard 5 marks Distance between two skew lines
• 26 Find the acute angle (in degrees, rounded to the nearest integer) between the line x = -1 + 2t, y = 3 - t, z = 4 + 3t and the plane 2x + y - 2z = 5. hard 4 marks Angle between a line and a plane
• 27 Find the shortest distance between the skew lines L_1:(x-1)/2=(y+2)/-3=(z-4)/5 and L_2:(x+2)/-1=(y-3)/4=(z+1)/2. hard 4 marks Shortest distance between skew lines
• 28 Find the acute angle (in degrees, rounded to the nearest integer) between the planes x-2y+3z=4 and 2x+y-z=0. hard MCQ 4 marks Angle between planes
• 29 Find the acute angle (in degrees, rounded to the nearest integer) between the line given by parametric equations x=2+t,;y=-1+2t,;z=4-t and the plane 3x+y-2z=5. medium 3 marks Angle between line and plane
• 30 Find the perpendicular distance of the point P(3,4,5) from the plane 2x-3y+z=10. easy 2 marks Distance from point to plane
• 31 Find the acute angle (in degrees, rounded to the nearest integer) between the line given by x=1+3t, y=-2+4t, z=2-t and the plane 2x-y+3z=5. medium 3 marks angle line–plane
• 32 Find the equation of the plane passing through the points A(0,1,2), B(2,-1,1) and C(1,3,0). hard 4 marks plane through three points
• 33 Find the perpendicular distance of the point P(2,-1,4) from the plane 3x-4y+2z=12. easy 2 marks Distance from point to plane
• 34 The acute angle between the planes 2x + y - 3z = 5 and x - 4y + 2z = 7 is closest to which value? medium MCQ 3 marks Angle between planes
• 35 Find the shortest distance between the skew lines L_1:(x-3)/4=(y+2)/-5=(z-1)/2 and L_2:(x+1)/-2=(y-4)/3=(z+3)/-1. hard 5 marks Shortest distance between skew lines
• 36 Find the equation of the plane that passes through the point (0,3,-1) and is parallel to the plane 4x - y + 3z = 8. medium 4 marks Plane through point parallel to given plane