3D Geometry
Showing 50 of 521 · 521 total
- 251.If two straight lines whose direction cosines are given by the relations l+m-n=0, 3l^2+m^2…Medium
- 252.Let the mirror image of the point (a,b,c) with respect to the plane 3x-4y+12z+19=0 be (a-6…Medium
- 253.Let the foot of the perpendicular from the point (1,2,4) on the line x+24=y-12=z+13 be P.Medium
- 254.The shortest distance between the lines x-32=y-23=z-1-1 and x+32=y-61=z-53 is:Medium
- 255.If two distinct points Q,R lie on the line of intersection of the planes -x+2y-z=0 and 3x-…Medium
- 256.The acute angle between the planes P_1 and P_2, when P_1 and P_2 are the planes passing th…Medium
- 257.Let the plane P: r a=d contain the line of intersection of the two planes r( i+3 j- k)=6 a…Medium
- 258.Let the plane ax+by+cz=d pass through (2,3,-5) and be perpendicular to the planes 2x+y-5z=…Medium
- 259.Let the image of the point P(1,2,3) in the line L: x-63=y-12=z-23 be Q.Medium
- 260.If the mirror image of the point (2,4,7) in the plane 3x-y+4z=2 is (a,b,c), then 2a+b+2c i…Medium
- 261.Let d be the distance between the feet of perpendiculars of the points P(1,2,-1) and Q(2,-…Medium
- 262.Let P_1: r(2 i+ j-3 k)=4 be a plane.Medium
- 263.Let Q be the mirror image of the point P(1,2,1) with respect to the plane x+2y+2z=16.Medium
- 264.Let a line having direction ratios 1,-4,2 intersect the lines x-73=y-1-1=z+21 and x2=y-73=…Medium
- 265.Let be the angle between the lines whose direction cosines satisfy the equations l+m-n=0 a…Medium
- 266.A line l passing through the origin is perpendicular to the lines [l_1: r=(3+t) i+(-1+2t) …Medium
- 267.The equation of the line through the point (0,1,2) and perpendicular to the line x-12=y+13…Medium
- 268.Let be an integer.Medium
- 269.Let a,b R.Medium
- 270.Consider the three planes P_1: 3x+15y+21z=9, P_2: x-3y-z=5, P_3: 2x+10y+14z=5.Medium
- 271.If the mirror image of the point (1,3,5) with respect to the plane 4x-5y+2z=8 is (,,), the…Medium
- 272.Let L be a line obtained from the intersection of two planes x+2y+z=6 and y+2z=4.Medium
- 273.Let (,2,1) be a point on the plane which passes through the point (4,-2,2).Medium
- 274.A plane passes through the points A(1,2,3), B(2,3,1), C(2,4,2).Medium
- 275.The vector equation of the plane passing through the intersection of the planes r( i+ j+ k…Medium
- 276.The distance of the point (1,1,9) from the point of intersection of the line x-31=y-42=z-5…Medium
- 277.The equation of the plane passing through the point (1,2,-3) and perpendicular to the plan…Medium
- 278.Let the position vectors of two points P and Q be 3 i- j+2 k and i+2 j-4 k respectively.Medium
- 279.If the foot of the perpendicular from the point (4,3,8) on the line L_1: x-al=y-23=z-b4, l…Medium
- 280.Let P be an arbitrary point having the sum of the squares of the distances from the planes…Hard
- 281.Let the plane ax+by+cz+d=0 bisect the line joining the points (4,-3,1) and (2,3,-5) at rig…Medium
- 282.The equation of the plane parallel to the plane x-2y+2z-3=0 which is at a unit distance fr…Medium
- 283.The equation of the plane which contains the Y-axis and passes through the point (1,2,3) i…Easy
- 284.If for a>0, the feet of perpendiculars from the points A(a,-2a,3) and B(0,4,5) on the plan…Medium
- 285.If (x,y,z) is an arbitrary point lying on a plane P, which passes through the points (42,0…Hard
- 286.If the equation of the plane passing through the line of intersection of the planes 2x-7y+…Medium
- 287.Let the mirror image of the point (1,3,a) with respect to the plane r(2 i- j+ k)-b=0 be (-…Medium
- 288.Let P be a plane containing the line x-13=y+64=z+52 and parallel to the line x-34=y-2-3=z+…Medium
- 289.Let P be a plane lx+my+nz=0 containing the line 1-x1=y+42=z+23.Medium
- 290.If the distance of the point (1,-2,3) from the plane x+2y-3z+10=0, measured parallel to th…Medium
- 291.If the lines x-k1=y-22=z-33 and x+13=y+22=z+31 are coplanar, then the value of k is: Answe…Medium
- 292.If the shortest distance between the straight lines 3(x-1)=6(y-2)=2(z-1) and 4(x-2)=2(y-)=…Medium
- 293.If the shortest distance between the lines r_1=( i+2 j+2 k)+( i-2 j+2 k), R, >0, and r_2=(…Medium
- 294.Let the plane passing through the point (-1,0,-2) and perpendicular to each of the planes …Medium
- 295.Let a,b,c be distinct positive numbers.Medium
- 296.Let a plane P pass through the point (3,7,-7) and contain the line x-2-3=y-32=z+21.Medium
- 297.For real numbers and 0, if the point of intersection of the straight lines x-1=y-12=z-13 a…Medium
- 298.The distance of the point P(3,4,4) from the point of intersection of the line joining the …Easy
- 299.Let the foot of perpendicular from a point P(1,2,-1) to the straight line L: x1=y0=z-1 be …Medium
- 300.Let L be the line of intersection of the planes r( i- j+2 k)=2 and r(2 i+ j- k)=2.Medium