Three Dimensional Geometry questions
879 published questions with worked solutions.
- The distance of the point (1, –2, 3) from the plane x – y + z = 5 measured parallel to a line, whose direction ratios are 2, 3,...
- Equation of a plane at a distance 2 21 for the origin, which contains the line of intersection of the planes x – y – z – 1 = 0...
- The equation of the plane passing through the line of intersection of the planes r .( i + j + k )=1 and r .(2 i +3 j + k )+4=0...
- Let S be the mirror image of the point Q(1, 3, 4) with respect to the plane 2x – y + z + 3 = 0 and let R(3, 5, ) be a point of...
- Let the equation of the plane, that passes through the point (1, 4, –3) and contains the line of intersection of the planes 3x...
- The square of the distance of the point of intersection of the line x-1 2 = y-2 3 = z+1 6 and the plane 2x – y + z = 6 from the...
- A plane passes through the points A(1, 2, 3), B(2, 3, 1) and C(2, 4, 2). If O is the origin and P is (2, –1, 1), then the...
- A line 'l' passing through origin is perpendicular to the lines l_1: r =(3+t) i +(-1+2t) j +(4+2t) k , l_2: r =(3+2s) i +(3+2s) j...
- The equation of the line through the point (0,1,2) and perpendicular to the line x-1 2 = y+1 3 = z-1 -2 is :
- Let be the angle between the lines whose direction cosines satisfy the equations l+m-n=0 and l^2+m^2-n^2=0. Then the value of ^4...
- If the lines x-k 1 = y+2 2 = z+3 3 are co-planar, then the value of k is________.
- Let the foot of perpendicular from a point P(1, 2, –1) to the straight line L : x 1 = y 0 = z -1 be N. Let a line be drawn from P...
- Let P be the plane passing through the point (1,2,3) and the line of intersection of the planes r ( i + j +4 k )=16 and r (- i +...
- Let Q be the foot of the perpendicular from the point P(7, –2, 13) on the plane containing the lines x+1 6 = y-1 7 = z-3 8 and...
- A plane P contain the line x + 2y + 3z + 1 = 0 = x – y – z – 6, and is perpendicular to the plane –2x + y + z + 8 = 0. Then which...
- Let the line L be the projection of the line x-1 2 = y-3 1 = z-4 2 in the plane x – 2y – z = 3. If d is the distance of the point...
- Let L be a line obtained from the intersection of two planes x + 2y + z = 6 and y + 2z = 4. If point P( , , ) is the foot of...
- If the mirror image of the point (1, 3, 5) with respect to the plane 4x – 5y + 2z = 8 is ( , , ), then 5( + + ) equals :
- If (1, 5, 35), (7, 5, 5), (1, , 7) and (2 , 1, 2) are coplanar, then the sum of all possible values of is
- Consider the three planes P_1: 3x + 15y + 21z = 9, P_2: x – 3y – z = 5, and P_3: 2x + 10y + 14z = 5 Then, which one of the...
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