3D Geometry
Showing 50 of 521 · 521 total
- 51.If the square of the shortest distance between the lines (x-2)/(1)=(y-1)/(2)=(z+3)/(-3) an…Medium
- 52.The distance of the line (x-2)/(2)=(y-6)/(3)=(z-3)/(4) from the point (1,4,0) along the li…Medium
- 53.Let P be the foot of the perpendicular from the point Q(10,-3,-1) on the line (x-3)/(7)=(y…Medium
- 54.Let a line pass through two distinct points P(-2,-1,3) and Q, and be parallel to the vecto…Medium
- 55.The perpendicular distance, of the line (x-1)/(2)=(y+2)/(-1)=(z+3)/(2) from the point P(2,…Medium
- 56.Let L_1:(x-1)/(2)=(y-2)/(3)=(z-3)/(4) and L_2:(x-2)/(3)=(y-4)/(4)=(z-5)/(5) be two lines.Medium
- 57.Consider the line L passing through the points (1,2,3) and (2,3,5).Medium
- 58.The shortest distance between the lines [(x-3)/(4)=(y+7)/(-11)=(z-1)/(5)] and [(x-5)/(3)=(…Medium
- 59.If the shortest distance between the lines (x- )/(2)=(y-4)/(3)=(z-3)/(4) and (x-2)/(4)=(y-…Medium
- 60.Let P(x, y, z) be a point in the first octant, whose projection in the x y-plane is the po…Medium
- 61.If the shortest distance between the lines array|c|c| L_1:r=(2+ )i+(1-3 )j+(3+4 )k, & R L_…Medium
- 62.Let P( , , ) be the image of the point Q(3,-3,1) in the line (x-0)/(1)=(y-3)/(1)=(z-1)/(-1…Medium
- 63.If A(3,1,-1),B((5)/(3),(7)/(3),(1)/(3)),C(2,2,1) and D((10)/(3),(2)/(3),(-1)/(3)) are the …Medium
- 64.The shortest distance between the lines [(x-3)/(2)=(y+15)/(-7)=(z-9)/(5)] and [(x+1)/(2)=(…Medium
- 65.Let ( , , ) be the image of the point (8,5,7) in the line (x-1)/(2)=(y+1)/(3)=(z-2)/(5).Medium
- 66.If the line (2-x)/(3)=(3y-2)/(4 +1)=4-z makes a right angle with the line (x+3)/(3 )=(1-2y…Medium
- 67.Let d be the distance of the point of intersection of the lines (x+6)/(3)=(y)/(2)=(z+1)/(1…Medium
- 68.Let P be the point of intersection of the lines (x-2)/(1)=(y-4)/(5)=(z-2)/(1) and (x-3)/(2…Medium
- 69.Let the point, on the line passing through the points P(1,-2,3) and Q(5,-4,7), farther fro…Medium
- 70.Consider a A B C where A(1,3,2), B(-2,8,0) and C(3,6,7).Medium
- 71.Let P and Q be the points on the line (x+3)/(8)=(y-4)/(2)=(z+1)/(2) which are at a distanc…Medium
- 72.If the mirror image of the point P(3,4,9) in the line (x-1)/(3)=(y+1)/(2)=(z-2)/(1) is (, …Medium
- 73.If the shortest distance between the lines (x- )/(-2)=(y-2)/(1)=(z-1)/(1) and x-√31=(y-1)/…Medium
- 74.Let ( , , ) be the mirror image of the point (2,3,5) in the line (x-1)/(2)=(y-2)/(3)=(z-3)…Medium
- 75.The shortest distance, between lines L_1 and L_2, where [L_1: (x-1)/(2)=(y+1)/(-3)=(z+4)/(…Medium
- 76.Let L_1:r=(i-j+2k)+ (i-j+2k), R, L_2:r=(j-k)+ (3i+j+pk), RL_3:r= (li+mj+nk), R be three li…Medium
- 77.Let ( , , ) be the foot of perpendicular from the point (1,2,3) on the line (x+3)/(5)=(y-1…Medium
- 78.Let A(2,3,5) and C(-3,4,-2) be opposite vertices of a parallelogram A B C D.Medium
- 79.Let P(3,2,3),Q(4,6,2) and R(7,3,2) be the vertices of .Medium
- 80.Let O be the origin and the position vectors of A and B be 2i+2j+k and 2i+4j+4k respective…Medium
- 81.Let PQR be a triangle with R(-1,4,2).Medium
- 82.Let the image of the point (1,0,7) in the line [(x)/(1)=(y-1)/(2)=(z-2)/(3)] be the point …Medium
- 83.The distance, of the point (7,-2,11) from the line (x-6)/(1)=(y-4)/(0)=(z-8)/(3) along the…Medium
- 84.If the shortest distance between the lines (x-4)/(1)=(y+1)/(2)=(z)/(-3) and (x-)/(2)=(y+1)…Medium
- 85.Let the foot of perpendicular of the point P(3,-2,-9) on the plane passing through the poi…Medium
- 86.Let the system of linear equations -x+2y-9z=7 -x+3y+7z=9 -2x+y+5z=8 -3x+y+13z= has a uniqu…Medium
- 87.Let S be the set of all values of , for which the shortest distance between the lines (x- …Medium
- 88.The line, that is coplanar to the line [(x+3)/(-3)=(y-1)/(1)=(z-5)/(5)], is :Medium
- 89.The plane, passing through the points (0,-1,2) and (-1,2,1) and parallel to the line passi…Medium
- 90.Let N be the foot of perpendicular from the point P(1,-2,3) on the line passing through th…Medium
- 91.Let the equation of plane passing through the line of intersection of the planes x+2 y+a z…Medium
- 92.The distance of the point (-1,2,3) from the plane r (i-2j+3k)=10 parallel to the line of t…Medium
- 93.Let the lines l_1:(x+5)/(3)=(y+4)/(1)=(z- )/(-2) and l_2:3x+2y+z-2=0=x-3y+2z-13 be coplana…Medium
- 94.Let the plane P: 4x-y+z=10 be rotated by an angle ( )/(2) about its line of intersection w…Hard
- 95.Let the line passing through the points P(2,-1,2) and Q(5,3,4) meet the plane x-y+z=4 at t…Medium
- 96.Let P be the plane passing through the points (5,3,0),(13,3,-2) and (1,6,2).Medium
- 97.Let ( , , ) be the image of the point P(2,3,5) in the plane 2x+y-3z=6.Easy
- 98.If equation of the plane that contains the point (-2,3,5) and is perpendicular to each of …Medium
- 99.Let the image of the point P(1,2,6) in the plane passing through the points A(1,2,0),B(1,4…Medium
- 100.Let the line [(x)/(1)=(6-y)/(2)=(z+8)/(5)] intersect the lines [(x-5)/(4)=(y-7)/(3)=(z+2)/…Medium