Three Dimensional Geometry questions
879 published questions with worked solutions.
- Let P_1: 2x+y-z=3 and P_2: x+2y+z=2 be two planes. Then, which of the following statement(s) is (are) TRUE?
- Let P be a point in the first octant, whose image Q in the plane x+y=3 (that is, the line segment PQ is perpendicular to the...
- Let L_1 and L_2 denote the lines r = i + (- i +2 j +2 k ), R and r = (2 i - j +2 k ), R respectively. If L_3 is a line which is...
- Three lines are given by r = i , R r = ( i + j ), R and r = ( i + j + k ), R . Let the lines cut the plane x+y+z=1 at the points...
- The distance of the point (x_1, y_1, z_1) from the line x - a = y - b = z - c is ..................
- The foot of the perpendicular from (0, 2, 3) to the line x + 3 5 = y - 1 2 = z + 4 3 is .....................
- The equations of the line joining the point (-2, 4, 2) and (7, -2, 5) are ..............
- If the direction ratios of a line are 1, -3, 2 then its direction cosines are.......
- The equation of the line joining the point (1, 2, 3) and parallel to the lines x - 4 2 = y + 1 -3 = z + 10 6 is ..........
- The equation of the line passing through origin and with d.r.s. 1, -1, 1 is given by, ..........
- A line making angle 45^ with each of X and Y-axis inclined with Z-axis at an angle.......
- The line x - 2 1 = y - 3 2 = z - 4 0 is .........
- The straight line x - l = y - m = z - 0 is perpendicular to ..............
- Let P(1, 2, 3), then d.c.s. of OP are ............
- If directions cosines of line are 1 c , 1 c , 1 c then c = ..........
- The lines x - 1 2 = y - 2 4 = z - 3 7 and x - 1 4 = y - 2 5 = z - 3 7 are ............ on the line
- The equation of the line passing through (1, 1, 1) and perpendicular to XZ-plane is.........
- For every point (x, y, z) on X-axis..........
- If the directions cosines of a line are 1 c , 1 c , - 1 c then ..........
- If l, m, n are direction cosines of a straight line then l^2 + m^2 + n^2 is ..........
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