Three Dimensional Geometry questions
879 published questions with worked solutions.
- The plane which bisects the line joining the points (4, –2, 3) and (2, 4, –1) at right angles also passes through the point -
- Let a plane P contain two lines r = i + ( i + j ), R and r =- j + ( j - k ), R. If Q ( , , ) is the foot of the perpendicular...
- Consider a ΔABC where A(1, 3, 2), B(−2, 8, 0) and C(3, 6, 7). If the angle bisector ∠BAC meets the line BC at D, then the length...
- If the mirror image of the point P(3, 4, 9) in the line x - 1 3 = y + 1 2 = z - 2 1 is (α, β, γ), then 14(α + β + γ) is:
- Let P and Q be the points on the line x + 3 8 = y - 4 2 = z + 1 2 which are at a distance of 6 units from the point R(1, 2, 3)....
- Let P the point of intersection of the lines x - 2 1 = y - 4 5 = z - 2 1 and x - 3 2 = y - 2 3 = z - 3 2 . Then, the shortest...
- Consider a line L passing through the points P(1, 2, 1) and Q(2, 1, −1). If the mirror image of the point A(2, 2, 2) in the line...
- Let the point, on the line passing through the points P(1, −2, 3) and Q(5, −4, 7), farther from the origin and at a distance of 9...
- Let d be the distance of the point of intersection of the lines x + 6 3 = y2 = z + 1 1 and x - 7 4 = y - 9 3 = z - 4 2 from the...
- If A(1, −1, 2), B(5, 7, −6), C(3, 4, −10) and D(−1, −4, −2) are the vertices of a quadrilateral ABCD, then its area is:
- If the line 2 - x 3 = 3y - 2 4 + 1 = 4 - z makes a right angle with the line x + 3 3 = 1 - 2y 6 = 5 - z 7 , then 4λ + 9μ is equal...
- Let (α, β, γ) be the image of the point (8, 5, 7) in the line x - 1 2 = y + 1 3 = z - 2 5 . Then α + β + γ is equal to
- If A(3, 1, −1), B ( 53, 73, 13 ), C(2, 2, 1) and D ( 10 3 , 23, -1 3 ) are the vertices of a quadrilateral ABCD, then its area is
- Let P be the point (10, −2, −1) and Q be the foot of the perpendicular drawn from the point R(1, 7, 6) on the line passing...
- Let P be a plane passing through the points (2, 1, 0), (4, 1, 1) and (5, 0, 1) and R be any point (2, 1, 6). Then the image of R...
- The mirror image of the point (1,2,3) in a plane is (- 7 3 ,- 4 3 ,- 1 3 ). Which of the following points lies on this plane ?
- A plane passing through the point (3, 1, 1) contains two lines whose direction ratios are 1, –2, 2 and 2, 3, –1 respectively. If...
- Let P(α, β, γ) be the image of the point Q(3, −3, 1) in the line x - 0 1 = y - 3 1 = z - 1 -1 and R be the point (2, 5, −1). If...
- The plane passing through the points (1, 2, 1), (2, 1, 2) and parallel to the line, 2x = 3y, z = 1 also passes through the point :
- The foot of the perpendicular drawn from the point (4, 2, 3) to the line joining the points (1, –2, 3) and (1, 1, 0) lies on the...
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