Introduction to Three-dimensional Geometry — practice questions
55 curated practice questions from Introduction to Three-dimensional Geometry (Mathematics Class 11, CBSE) — 43 easy, 12 medium. Every question includes the final answer free; step-by-step worked solutions with a free account.
- Find the coordinate of the point P which is five-sixth of the way from A (–2, 0, 6) to B (10, –6, –12).
- The point which divides the line joining the points (1, 3, 4) and (4, 3, 1) internally in the ratio 2 : 1, is
- Statement-I : Coordinates of centroid of a triangle formed by the vertices A (3, 2, 0), B (5, 3, 2) and C (0, 2, 4) is…
- Find the equation of the set of the points P such that its distances from the points A (3, 4, –5) and B (–2, 1, 4) are…
- Find the coordinates of the point which is three fifth of the way from (3, 4, 5) to (–2, –1, 0).
- Distance of the point (3, 4, 5) from the origin (0, 0, 0) is
- If two vertices of a triangle are (4, 2, 1) and (5, 1, 4). If the centroid is (5, 2, 3), then the third vertex is
- The distance of the point A (2, 3, 2) from the x -axis is
- If the origin is the centroid of the triangle with vertices A (3 a , 4, –5), B (–2, 4 b , 6) and C (6, 10, c ), then…
- Find the equation of set of points P such that PA 2 + PB 2 = 2 k 2 , where A and B are the points (3, 4, 5) and (–1, 3…
- The distance of point P (3, 4, 5) from the yz -plane is
- Statement-I : The points A (1, –1, 3), B (2, –4, 5) and C (5, –13, 11) are collinear. Statement-II : If AB + BC = AC …
- Statement-I : The points A (3, –1, 2), B (1, 2, – 4), C (–1, 1, 2) and D (1, –2, 8) are the vertices of a…
- The perpendicular distance of the point (8, 15, 6) from y -axis is
- Statement-I : The distance between the points and (1, –2, 3) is units. Statement-II : Distance between any two points A…
- The centroid of a triangle ABC is at the point (1, 1, 1). If the coordinates of A and B are (3, –5, 7) and (–1, 7, –6)…
- The distance of the point A (2, 3, 4) from the y -axis is
- The points A (3, 2, 0), B (5, 3, 2) and C (0, 2, 4) are the vertices of a triangle. Find the distance of the point A…
- If P (3, 2, – 4), Q (5, 4, – 6) and R (9, 8, – 10) are collinear, then R divides PQ in the ratio
- Find the distance between the points P (1, –3, 4) and Q (–4, 1, 2).
- In the given figure, if P is (2, 4, 5), find the coordinates of F .
- Find the coordinates of the centroid of the triangle whose vertices are ( x 1 , y 1 , z 1 ), ( x 2 , y 2 , z 2 ) and (…
- Find the octant in which the points (–3, 1, 2) and (–3, 1, –2) lie respectively.
- Let A (3, 2, 0), B (5, 3, 2), C (–9, 6, –3) be three points forming a triangle. AD , the bisector of ∠ BAC , meets BC…
- Let A , B , C be the feet of the perpendicular segments drawn from a point P (3, 4, 5) on the xy , yz and zx -planes…
- A point R with x -coordinate 4 lies on the line segment joining the points P (2, –3, 4) and Q (8, 0, 10). Find the…
- The distance of the point P ( a , b , c ) from the x -axis is
- L is the foot of the perpendicular drawn from a point (3, 5, 6) on x -axis. The coordinates of L are
- Statement-I : The foot of perpendicular drawn from the point A (1, 2, 8) on the xy -plane is (1, 2, 0) Statement-II …
- The coordinates of a point which divides the line joining A (2, 5, 7) and B (1, 3, 0) in the ratio 2 : 1 are
- What is the perpendicular distance of the point P (6, 7, 8) from xy -plane?
- The points A (4, – 2, 1), B (7, – 4, 7), C (2, – 5, 10) and D (– 1, – 3, 4) are the vertices of a
- Find the coordinates of the point which divides the line segment joining the points (1, –2, 3) and (3, 4, –5) in the…
- M is the foot of the perpendicular drawn from the point A (6, 7, 8) on the yz -plane. What are the coordinates of point…
- Find the ratio in which the line segment joining the points (4, 8, 10) and (6, 10, –8) is divided by the yz -plane.
- The point in the xy -plane which is equidistant from the points (5, 0, 6), (0, –3, 2) and (4, 5, 0) is
- Determine the point in yz -plane which is equidistant from three points A (2, 0, 3), B (0, 3, 2) and C (0, 0, 1).
- Ratio in which the xy -plane divides the join of (1, 2, 3) and (4, 2, 1) is
- Find the point on x -axis which is equidistant from the point A (3, 2, 2) and B (5, 5, 4).
- Find the coordinates of the points which trisect the line segment AB where A (2, 1, –3) and B (5, –8, 3)
- Let A , B , C be the feet of the perpendicular segments drawn from a point P (3, 4, 5) on the xy , yz and zx -planes…
- Find the ratio in which the line segment joining the points (2, 4, 5) and (3, 5, –4) is divided by the xz -plane.
- The perpendicular distance of the point (6, 5, 8) from z -axis is
- L is the foot of the perpendicular drawn from a point P (3, 4, 5) on the xy -plane. The coordinates of point L are
- A plane is parallel to yz -plane so it is perpendicular to :
- Find the point on y -axis which is at a distance of units from the point (1, 2, 3).
- L is the foot of the perpendicular drawn from a point (3, 4, 5) on x -axis. The coordinates of L are
- Mid-point of the line joining the points (– 1, 2, 3) and (2, – 1, 3) is
- Let L , M , N be the feet of the perpendiculars drawn from a point P (7, 9, 4) on the x , y and z -axes respectively…
- Find the points of trisection of the segment joining the points A (1, 0, –6) and B (–5, 9, 6).
- The ratio in which the join of (1, – 2, 3) and (4, 2, – 1) is divided by the xy plane is
- The locus of a point for which y = 0, z = 0 is
- Find the coordinates of a point equidistant from the four points O (0, 0, 0), A ( l , 0, 0), B (0, m , 0) and C (0, 0…
- What is the locus of a point for which x = 0, z = 0?
- What is the length of foot of perpendicular drawn from the point P (3, 4, 5) on y -axis?