Three Dimensional Geometry questions
879 published questions with worked solutions.
- The equation of the plane bisecting the angle between the planes 3x+4y=4 and 6x-2y+3z+3=0 that contains the origin, is
- The direction cosines of the projection of the line x -2 = y-1 1 = z+1 -1 on the plane 2x+y-3z=5 are
- Two systems of rectangular axes have the same origin. If a plane cuts them at distances a,b,c and a',b',c' from the origin then
- The lines x=ay+b, z=cy+d and x=a'y+b', z=c'y+d' will be perpendicular if and only if
- Which of the following planes intersects the planes x-y+2z=3 and 4x+3y-z=1 along the same line?
- The line x-1 2 = y -1 = z+2 2 cuts the plane x+y+z=1 at P. If the foot of the perpendicular from P to a plane be (3,-4,1) then...
- A variable plane at a distance of 1 unit from the origin cuts the coordinate axes at A, B and C. If the centroid D(x,y,z)...
- A plane through the line x-1 1 = y+1 -2 = z1 has the equation
- The equation of a plane is 2x-y-3z=5 and A(1,1,1), B(2,1,-3), C(1,-2,-2) and D(-3,1,2) are four points. Which of the following...
- A point on the line x-1 0 = y 1 = z+1 2 at a distance 3 from the plane x+y+z=3 is
- The lines x-2 1 = y-3 1 = z-4 -k and x-1 k = y-4 2 = z-5 1 are coplanar if k is
- If the angle between the line x+1 1 = y-1 2 = z-2 2 and the plane 2x-y+ z+4=0 is such that = 13 then the value of is
- In each question, match every entry of Column I with the correct entry of Column II. (An entry of Column II may be used more than...
- In each question, match every entry of Column I with the correct entry of Column II. (An entry of Column II may be used more than...
- A plane exists which is perpendicular to the line x 3 = y-1 5 = z+1 7 and passes through the line x+3 10 = y-1 -20 = z+1 k . Then...
- The equations of two straight lines are x-1 2 = y+3 1 = z-2 -3 and x-2 1 = y-1 -3 = z+3 2 . STATEMENT-1: The given lines are...
- Let P(4, 1, ) and Q(2, -1, ) be two points. A line having direction ratios 1, -1, 6 is perpendicular to the plane passing through...
- A plane parallel to x + y + z = 3 and at distance 4 3 from it has the equation
- Three lines OA, OB and OC through the origin O have direction ratios l, 2, 1; 1, m, 2 and 2, 1, n respectively. Column I: (i) OB...
- A line with direction ratios 2, 1, 2 meets the lines x = y + a = z and x + a = 2y = 2z at P and Q, respectively. Then the length...
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