Three Dimensional Geometry questions
879 published questions with worked solutions.
- The value of m, such that x-4 1 = y-2 1 = 2z-m 3 lies in the plane 2x-5y+2z=7, is
- Equation of the plane containing the straight line x3= y2= z4 and perpendicular to the plane containing the straight lines x4=...
- If the points (1,-1, ) and (-3,0,1) are equidistant from the plane 3x - 4y - 12z + 13 = 0, then the sum of all possible values of...
- Let P be a plane passing through the points (2,1,0), (4,1,1) and (5,0,1), and R be the point (2,1,6). Then image of R in the...
- The equation of the plane, passing through the point (-1, 2, -3) and parallel to the lines x-1 3 = y-2 2 = z -4 and x 2 = y-1 -3...
- The co-ordinates of the point where the line through A(3,4,1) and B(5,1,6) crosses the xy-plane are
- A plane which is perpendicular to two planes 2x – 2y + z = 0 and x – y + 2z = 4, passes through (1,-2,1). The distance of the...
- Let a= i+3 j- k, b=3 i- j+4 k and c= i+2 j-2 k, (where , IR, be three vectors. If the projection of a on c is 10 3 and b c=-6...
- The lines x-2 1 = y-3 1 = z-4 -k and x-1 k = y-4 2 = z-5 1 are coplanar if
- The length of the perpendicular from the origin to the plane r (3 i-4 j+12 k)=8 is
- The direction cosines of the line which is perpendicular to the two lines x-7 2 = y+17 -3 = z-6 1 and x+7 1 = y+3 2 = z-6 -2 are
- The equation of the plane passing through the points (1, 2, 3), (-1, 4, 2) and (3, 1, 1) is
- If the area of the triangle with vertices i+y j, i+2 k and 3 i+ k is 6 sq. units, then the values of y are
- If the planes r (2 i- j+ k )=3 and r (4 i- j+ k )=5 are parallel, then values of and are respectively
- If the line passing through the points (a,1,6) and (3,4,b) crosses the yz - plane at the point (0, 17 2 , -13 2 ), then
- The co-ordinates of the foot of the perpendicular drawn form the origin to the plane 2x + 6y - 3z = 63 are
- The sum of the lengths of projections of p i + q j + r k on the co-ordinate axes, where p = 4, q = -5, r = 7 is
- The equation of the plane through the intersection of the planes x + y + z = 1 and 2x + 3y – z + 4 = 0 and parallel to X –axis is
- A plane is parallel to two lines whose direction ratios are (1, 0, -1) and (-1, 1, 0) and it contains the point (1, 1, 1). If it...
- The equation of the line passing through the point (-1, 3, -2) and perpendicular to each of the lines x 1 = y 2 = z 3 and x+2 -3...
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