3D Geometry
Showing 50 of 521 · 521 total
- 101.The shortest distance between the lines (x+2)/(1)=(y)/(-2)=(z-5)/(2) and (x-4)/(1)=(y-1)/(…Medium
- 102.Let two vertices of a triangle ABC be (2, 4, 6) and (0, -2, -5), and its centroid be (2, 1…Medium
- 103.Let P be the point of intersection of the line (x+3)/(3)=(y+2)/(1)=(1-z)/(2) and the plane…Medium
- 104.For a,b Z and |a-b| 10, let the angle between the plane P:ax+y-z=b and the line l:x-1=a-y=…Medium
- 105.Let P be the plane passing through the line (x-1)/(1)=(y-2)/(-3)=(z+5)/(7) and the point (…Medium
- 106.The shortest distance between the lines [(x-4)/(4)=(y+2)/(5)=(z+3)/(3)] and [(x-1)/(3)=(y-…Medium
- 107.If the equation of the plane containing the line x+2 y+3 z-4=0=2 x+y-z+5 and perpendicular…Medium
- 108.A plane P contains the line of intersection of the plane r (i+j+k)=6 and r (2i+3j+4k)=-5.Medium
- 109.Let the line L pass through the point (0,1,2), intersect the line (x-1)/(2)=(y-2)/(3)=(z-3…Medium
- 110.If the equation of the plane passing through the line of intersection of the planes 2 x-y+…Medium
- 111.One vertex of a rectangular parallelopiped is at the origin O and the lengths of its edges…Medium
- 112.Let the plane P:8x+ _1y+ _2z+12=0 be parallel to the line L:(x+2)/(2)=(y-3)/(3)=(z+4)/(5).Medium
- 113.Let P be the plane, passing through the point (1,-1,-5) and perpendicular to the line join…Medium
- 114.If a point P( , , ) satisfying (gathered gathered)((|gathered 2 10 8 9 3 8 8 4 8 gathered)…Medium
- 115.A vector v in the first octant is inclined to the x-axis at 60^ , to the y-axis at 45 and …Medium
- 116.If a plane passes through the points (-1, k, 0),(2, k,-1),(1,1,2) and is parallel to the l…Medium
- 117.Let a line L_1 pass through the origin and be perpendicular to the lines L_2: r=(3+t)i+(2t…Medium
- 118.Let the image of the point P(0,-5,0) in the line (x-1)/(2)=(y)/(1)=(z+1)/(-2) be the point…Medium
- 119.Let a line L passing through the point P(1,1,1) be perpendicular to the lines (x-4)/(4)=(y…Medium
- 120.If the image of the point P(a,2,a) in the line (x)/(2)=(y+a)/(1)=(z)/(1) is Q and the imag…Medium
- 121.Let the area of the triangle formed by the lines x+2=y-1=z, (x-3)/(5)=(y)/(-1)=(z-1)/(1) a…Medium
- 122.Let P be the image of the point Q(7,-2,5) in the line L:(x-1)/(2)=(y+1)/(3)=(z)/(4) and R(…Medium
- 123.Let L_1:(x-1)/(3)=(y-1)/(-1)=(z+1)/(0) and L_2:(x-2)/(2)=(y)/(0)=(z+4)/( ), R, be two line…Medium
- 124.The square of the distance of the image of the point (6,1,5) in the line [(x-1)/(3)=(y)/(2…Medium
- 125.Let P( , , ) be the image of the point Q(1,6,4) in the line (x)/(1)=(y-1)/(2)=(z-2)/(3).Medium
- 126.If the shortest distance between the lines (x- )/(3)=(y-2)/(-1)=(z-1)/(1) and (x+2)/(-3)=(…Medium
- 127.Let P be the point (10,-2,-1) and Q be the foot of the perpendicular drawn from the point …Medium
- 128.Let the point (-1, , ) lie on the line of the shortest distance between the lines (x+2)/(-…Medium
- 129.Consider a line L passing through the points P(1,2,1) and Q(2,1,-1).Medium
- 130.Let the line of the shortest distance between the lines gathered L_1: r=(i+2j+3k)+ (i-j+k)…Medium
- 131.A line passes through A(4,-6,-2) and B(16,-2,4).Medium
- 132.Let Q and R be the feet of perpendiculars from the point P(a,a,a) on the lines x=y,z=1 and…Medium
- 133.Let a line passing through the point (-1,2,3) intersect the lines [L_1: (x-1)/(3)=(y-2)/(2…Medium
- 134.If d_1 is the shortest distance between the lines x+1=2y=-12z,x=y+2=6z-6 and d_2 is the sh…Medium
- 135.Let O be the origin, and M and N be the points on the lines (x-5)/(4)=(y-4)/(1)=(z-5)/(3) …Medium
- 136.A line with direction ratios 2,1,2 meets the lines x=y+2=z and x+2=2 y=2 z respectively at…Medium
- 137.The lines [(x-2)/(2)=(y)/(-2)=(z-7)/(16)] and [(x+3)/(4)=(y+2)/(3)=(z+2)/(1)] intersect at…Medium
- 138.Let the plane P contain the line 2 x+y-z-3=0=5 x-3 y+4 z+9 and be parallel to the line (x+…Medium
- 139.Let the image of the point ((5)/(3),(5)/(3),(8)/(3)) in the plane x-2y+z-2=0 be P.Medium
- 140.Let the plane x+3 y-2 z+6=0 meet the co-ordinate axes at the points A, B, C.Medium
- 141.Let the line l:x=(1-y)/(-2)=(z-3)/( ), R meet the plane P:x+2y+3z=4 at the point ( , , ).Medium
- 142.Let a line l pass through the origin and be perpendicular to the lines l_1:r=(-11-7k)+ (i+…Medium
- 143.Let the foot of perpendicular from the point A(4,3,1) on the plane P:x-y+2z+3=0 be N.Medium
- 144.Let P_1 be the plane 3x-y-7z=11 and P_2 be the plane passing through the points (2,-1,0),(…Medium
- 145.Let _1, _2 be the values of for which the points ((5)/(2),1, ) and (-2,0,1) are at equal d…Medium
- 146.If the lines (x-1)/(2)=(2-y)/(-3)=(z-3)/( ) and (x-4)/(5)=(y-1)/(2)=(z)/( ) intersect, the…Medium
- 147.Let the image of the point P(1,2,3) in the plane 2x-y+z=9 be Q.Medium
- 148.Let a line L pass through the point P(2,3,1) and be parallel to the line x+3 y-2 z-2=0=x-y…Medium
- 149.If the image of the point P(a, 2, a) in the line L_1: x2=y+a1=z1 is Q, and the image of Q …Hard
- 150.Let a line L passing through the point P(1,1,1) be perpendicular to the lines L_1: x-44=y-…Hard