3D Geometry
Showing 50 of 521 · 521 total
- 451.A plane which passes through the point (3,2,0) and the line x-41=y-75=z-44 isMedium
- 452.The d.r. of normal to the plane through (1, 0, 0), (0, 1, 0) which makes an angle [ /4] wi…Medium
- 453.A line makes the same angle [ ], with each of the x and z axis.Medium
- 454.If the angel [ ] between the line [x + 1 1 = y - 1 2 = z - 2 2] and the plane [2x - y + ,,…Medium
- 455.The distance between the line [ r = 2 i - 2 j + 3 k + ( i - j + 4k ),] and the plane [ r .…Medium
- 456.The two lines x=ay+b, z=cy+d; and x=a'y+b' , z=c'y+d' are perpendicular to each other if :Medium
- 457.If (2,3,5) is one end of a diameter of the sphere [x^2 + y^2 + z^2 - 6x - 12y - 2z + 20 = …Medium
- 458.The projections of a vector on the three coordinate axis are 6,-3,2 respectively.Easy
- 459.A equation of a plane parallel to the plane x-2y+2z-5=0 and at a unit distance from the or…Medium
- 460.If the image of the point P(1, --2, 3) in the plane, 2x + 3y -- 4z + 22 = 0 measured paral…Medium
- 461.If the line, [x - 3 1 = y + 2 - 1 = z + - 2] lies in the plane, 2x-4y+3z=2, then the short…Medium
- 462.An angle between the lines whose direction cosines are gien by the equations, l + 3m + 5n …Hard
- 463.A variable plane passes through a fixed point (3,2,1) and meets x, y and z axes at A, B an…Medium
- 464.If the angle between the lines, [x 2 = y 2 = z 1] and [5 - x - 2 = 7y - 14 p = z - 3 4,,] …Medium
- 465.If the plane 2x -- y + 2z + 3 = 0 has the distances [1 3] and [2 3] units from the planes …Medium
- 466.If the length of the perpendicular from the point ([ ], 0, [ ]) ([ ] [ ] 0) to the line, […Medium
- 467.The plane passing through the point (4, --1, 2) and parallel to the lines [x + 2 3 = y - 2…Medium
- 468.Let A be a point on the line [ r = ( 1 - 3 ) i + ( - 1 ) j + ( 2 + 5 ) k] and B(3, 2, 6) b…Medium
- 469.The magnitude of the projection of the vector [ 2i^ + 3j^ + k^ ] on the vector perpendicul…Medium
- 470.The vertices B and C of a [ ]ABC lie on the line, [x + 2 3 = y - 1 0 = z 4] such that BC =…Medium
- 471.The equation of the plane containing the straight line [x 2 = y 3 = z 4] and perpendicular…Medium
- 472.If (a, b, c) is the image of the point (1, 2, -3) in the line [x + 1 2 = y - 3 - 2 = z - 1…Medium
- 473.The mirror image of the point (1, 2, 3) in a plane is [( - 7 3, - 4 3, - 1 3 )].Medium
- 474.Let [] be the angle between the lines whose direction cosines satisfy the equations l + m …Medium
- 475.Consider the three planes P1 : 3x + 15y + 21z = 9, P2 : x - 3y - z = 5, and P3 : 2x + 10y …Medium
- 476.If (1, 5, 35), (7, 5, 5), (1, [], 7) and (2[], 1, 2) are coplanar, then the sum of all pos…Medium
- 477.A plane E is perpendicular to the two planes 2 x-2 y+z=0 and x-y+2 z=4, and passes through…Medium
- 478.The shortest distance between the lines [(x+7)/(-6)=(y-6)/(7)=z] and [(7-x)/(2)=y-2=z-6] i…Medium
- 479.Let [P] be the plane containing the straight line [(x-3)/(9)=(y+4)/(-1)=(z-7)/(-5)] and pe…Medium
- 480.Let Q be the mirror image of the point P(1, 0, 1) with respect to the plane S : x + y + z …Medium
- 481.A vector [a] is parallel to the line of intersection of the plane determined by the vector…Medium
- 482.The length of the perpendicular from the point (1,-2,5) on the line passing through (1,2,4…Medium
- 483.If the lines [ r = ( i - j + k ) + ( 3 j - k )] and [ r = ( i - j ) + ( 2 i - 3 k )] are c…Medium
- 484.Let [ a = i + j + 2 k], [ b = 2 i - 3 j + k] and [ c = i - j + k] be three given vectors.Medium
- 485.Let the plane 2x + 3y + z + 20 = 0 be rotated through a right angle about its line of inte…Hard
- 486.If the length of the perpendicular drawn from the point P(a, 4,2), a >0 on the line [(x+1)…Hard
- 487.If the line of intersection of the planes a x+b y=3 and a x+b y+c z=0, a >0 makes an angle…Medium
- 488.If the plane P passes through the intersection of two mutually perpendicular planes 2 x+k …Medium
- 489.If two straight lines whose direction cosines are given by the relations l + m - n = 0, 3l…Medium
- 490.Let the lines [(x-1)/()=(y-2)/(1)=(z-3)/(2)] and [(x+26)/(-2)=(y+18)/(3)=(z+28)/()] be cop…Medium
- 491.A plane P is parallel to two lines whose direction ratios are -2,1,-3 and -1,2,-2 and it c…Medium
- 492.The foot of the perpendicular from a point on the circle x^2+y^2=1, z=0 to the plane 2 x+3…Medium
- 493.The acute angle between the planes P1 and P2, when P1 and P2 are the planes passing throug…Medium
- 494.Let the plane [P: r ,., a = d] contain the line of intersection of two planes [ r ,.,( i +…Medium
- 495.Let Q be the foot of perpendicular drawn from the point P(1,2,3) to the plane x+2 y+z=14.Medium
- 496.If [(2,3,9),(5,2,1),(1, , 8)] and [(, 2,3)] are coplanar, then the product of all possible…Medium
- 497.If the foot of the perpendicular from the point [A(-1,4,3)] on the plane [P: 2 x+m y+n z=4…Medium
- 498.The distance of the point (3, 2, -1) from the plane 3x - y + 4z + 1 = 0 along the line [2 …Medium
- 499.Let the line [(x)/(1)=(6-y)/(2)=(z+8)/(5)] intersect the lines [(x-5)/(4)=(y-7)/(3)=(z+2)/…Medium
- 500.Let the line passing through the points [P(2,-1,2)] and [Q(5,3,4)] meet the plane x-y+z=4 …Medium