Plus One Maths Chapter Wise Previous Questions Chapter 12 Introduction to Three Dimensional Geometry

Kerala Plus One Maths Chapter Wise Previous Questions Chapter 12 Introduction to Three Dimensional Geometry

Plus One Maths Three Dimensional Geometry 3 Marks Important Questions

Question 1.
Consider the triangle with vertices (0,7,- 10), (1,6,- 6) and (4,9,- 6) (MARCH-2010)
i) Find the sides AB, BC and CA.
ii) Prove that the triangle is right triangle.
iii) Find the centroid of the triangle.
Answer:

Question 2.
i) Find the co-ordinates of the points which trisect the line segment joining the points P(4,0,1) and Q(2,4,0). (IMP-2010)
ii) Find the locus Of the set of points P such that the distance from A(2,3,4) is equal to twice the distance from B(-2,1,2).
Answer:
i)

Let R and S be two points which trisect the line join of PQ. Therefore PR = RS = SQ

Question 3.
i) Write the coordinate of the centroid of the triangle whose vertices are
(x₁, y₁, z₁) ; (x₁, y₁, z₁)and(x₁, y₁, z₁) (IMP-2011)
ii) If the centroid of the triangle ABC is (1,1,1) and A and B are (3,-5,7), (1,1,2) then find the coordinate of C.
Answer:

Question 4.
Given three points A(- 4,6,10), B(2,4,6) and C(14,0,- 2) (IMP-2012)
i) Find AB.
ii) Prove that the points A, B and C are collinear.
Answer:
i)

ii)

Question 5.
Name the octants in which the points A(1,6,- 6) and B(- 1,- 6,- 6). Find the distance between A and B. (IMP-2012)
Answer:
ASP A(1,6,- 6) and B(-1 ,-6,-6) in the octants XOYZ’ and X’OY’Z’ respectively.

Question 6.
i) If P is a point in YZ-plane, then its x coordinate is ………….. (IMP-2013)
ii) Find the ratio in which the YZ-plane divides the line segment formed by joining the points (-2,4,7) and (3,-5,8).
Answer:
i) Zero
ii) Let the ratio be kA. Since the point lies on the YZ plane, its x-coordinate. will be zero. Hence

Therefore the ratio is 2:3.

Question 7.
i) Find the distance between the points (2- 1,3) and (- 2,1,3) (MARCH-2013)
ii) Find the coordinate 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.
Answer:

Question 8.
i) Name the octant in which the points (3,- 2,1) and (- 5,- 6,1) lie. (MARCH-2014)
ii) Find the distance between the points P(1,- 3,4) and Q(- 4,1,2).
(March(Commerce) – 2014)
Answer:
i) (3,-2,1) lie on octant XOYZ and (-5,-6,1) lie on octant X’OY’Z.
ii)

Question 9.
Find the centroid of the triangle with vertices (3,- 5,7), (- 1,7,- 6) and (1,1,2). (IMP-2010)
Answer:

= (1,1,1)

Question 10.
Show that the points (-2,3,5), (1,2,3) and (7,0,-1) are collinear. (IMP-2014)
Answer:

Question 11.
Find the coordinate of the points which divides the line segment joining the points (- 2,3,5) and (1,- 4,6) in the ration 2 : 3 internally. (IMP-2014)
Answer:
coordinate of the point is:

Question 12.
i) State whether the following is TRUE or FALSE. (MAY-2017)
“The point (4,-2,-5) lies in the eight octant.”
ii) Find the equation of the set of points such that its distances from the points A (3,4,- 5) and B (- 2,1,4) are equal.
Answer:
i) True
ii) PA = PB

Question 13.
i) The distance between the point (1,-2,3) and (4,1,2) is …………. (MARCH-2017)
(a) √2
(b) √19
(c) √11
(d) √15
ii) the centroid of the 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.
Answer:
i) (b) √19
ii)

Plus One Maths Three Dimensional Geometry 4 Marks Important Questions

Question 1.
Consider the points A(- 2,3,5), B(1,2,3) and C(7,0,- 1) (MARCH-2011)
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.
Answer:

Question 2.
i) The x – coordinate of the point in the YZ plane is ………….. (MARCH-2013)
ii) Find the ratio in which the YZ plane divides the line segment joining the points (- 2,4,7) and (3,- 5,8).
Answer:
i) zero
ii) Let the ratio be k:1. Since the point lies on the YZ plane, its Xrcoordinate will be zero. Hence

Question 3.
i) Find the distance between the points (2,3,5) and (4,3,1). (MARCH-2014)
ii) Find the ratio in which the line segment joining the points A(4,8,10) and B (6,10,-8) is divided by the XY plane. (March (Science) – 2014)
Answer:

Question 4.
A point in the XZ plane is (MARCH-2015)
a) (1,1,1)
b) (2,0,3)
c) (2,3,0)
d) (-1,2,3)
ii) 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.
Answer:


Here; AB = CD and BC = DA, therefore ABCD is a parallelogram

Question 5.
i) Which of the following lies in the sixth octant? (MARCH-2016)
a) (- 3,- 2,- 2)
b) (- 3,1,- 2)
c) (3,- 1,2)
d) (3,- 1,-2)
ii) Find the ratio in which the YZ plane divides the line joining the points (- 2, 4, 7) and (3,- 5,8)
Answer:
i) b) (- 3,1,- 2)
ii) Let the ratio be k:1. Since the point lies on the YZ plane, its Xrcoordinate will be zero. Hence

Question 6.
i) Which one of the following points lies in the sixth octant? (IMP-2015)
a) (-4,2,-5)
b) (-4,-2,-5)
c) (4,-2,-5)
d) (4,2,5)
ii) Find the ratio in which the YZ plane divides the line segment formed by joining the points (-2,4,7) and (3,-5,8).
Answer:
i) a) (-4,2,-5)
ii) Let the line joining the points A(-2,4,7) and B(3,-5, 8) is divided by the yz-plane in the ratio k: 1.
Then the coordinate

Plus One Maths Three Dimensional Geometry 6 Marks Important Questions

Question 1.
i) If \(\left(\frac{5}{3}, \frac{22}{3}, \frac{-22}{3}\right)\) is the centriod of is the centroid of ∆PQR with vertices P(a,7,-10), Q(1,2b,-6) and R(4,9,3c), Find the value of a, b, c. (MARCH-2012)
ii) Prove that ∆PQR is isosceles.
Answer:

Plus One Maths Chapter Wise Previous Questions and Answer