Kerala Plus One Maths Chapter Wise Previous Questions and Answers Chapter 12 Introduction to Three Dimensional Geometry
Consider a point A(4,8,10) in space.
a. Find the distance of the point A from XY- plane.
b. Find the distance of the point A from X – axis.
c. Find the ratio in which the line segment joining the point A and B (6,10, -8) is divided by YZ -plane.
a. 10 [Z coordinate of the point]
Let P(4,0,0) be a line on the X-axis.
a. The distance between the points (1, -2,3) and (4,1,2) is
b. The centroid of a triangle ABC is at the point (1, 2, 3). If the coordinates of A and B are (3, -5, 7)
and (-1, 7, -6) respectively. Find the coordinates of the point C. [March-2017]
a. Which one of the following points lies in the sixth octant?
b. Find the ratio in which the YZ plane divides the line segment formed by joining the points (-2,4,7)
and (3, -5,8). [March-2016]
a.i. (-4, 2, -5)
Let YZ plane divides the line joining the points A (-2, 4, 7) and B (3, -5, 8) at R (x, y, z) in the ratio k: 1.
Then x coordinates of R = 0.
a. A point in the XZ plane is………………
b. Show that the points A (1, 2, 3), B (-1, -2,-1), C (2,3,2) and D (4,7,6) are the vertices of a parallelogram. [March-2015]
a. Find the distance between the points (2,3,5) and (4,3,1).
b. Find the ratio in which the line segment joining the points A (4, 8, 10) and B (6,10,-8) 9s divided by the XY plane.[March-2014]
a. Find the distance between the points (2,-1,3) and (-2,1,3).
b. Find the coordinates of the point which divides the line segment joining the points (-2, 3, 5) and (1, -4, 6) internally in the ratio of 2:3. [March-2013]
Given three points A(-4,6,10), B (2,4,6) and C (14,0,2).
i. Find AB,BC and AC.
ii. Prove that A, B and C are nonlinear. [February-2013]
If is the centroid of ΔPQR
with vertices P (a, 7, -10), Q (1, 2b, -6), R (4,9,3c) find the values of a, b, and c.
b. Prove that A PQR is isosceles. [March-2012]
Consider the points A (-2,3,5), B (1,2,3) and C (7,0,-1).
i. Using the distance formula, show that the points A, B and C are collinear.
ii. Find the ratio in which B divides the line segment AC. [March-2011]
Consider the points A (-2, 4, 7) and B (3,-5,8).
i. If P divides AB in the ratio k: 1, then find the coordinates of P.
ii. Find the co-ordinates of the point where the line segment AB crosses the YZ-plane. [August-2009]
i. Section formulae,
Consider the points A (2,1,3) and B (1,2,1).
a. Find the ratio in which the join of AB is divided by YZ plane.
b. Also find the point of division. [March-2009]
a. Any point on the YZ plane is (0, y, z) Let this point divides the line joining (2,1,3) and B (1,2,1) in the ratio m: n