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

Kerala State Board New Syllabus Plus One Maths Chapter Wise Previous Questions and Answers 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:
Plus One Maths Chapter Wise Previous Questions Chapter 12 Introduction to Three Dimensional Geometry 1

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)
Plus One Maths Chapter Wise Previous Questions Chapter 12 Introduction to Three Dimensional Geometry 2
Let R and S be two points which trisect the line join of PQ. Therefore PR = RS = SQ
Plus One Maths Chapter Wise Previous Questions Chapter 12 Introduction to Three Dimensional Geometry 3

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:
Plus One Maths Chapter Wise Previous Questions Chapter 12 Introduction to Three Dimensional Geometry 4

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)
Plus One Maths Chapter Wise Previous Questions Chapter 12 Introduction to Three Dimensional Geometry 5
ii)
Plus One Maths Chapter Wise Previous Questions Chapter 12 Introduction to Three Dimensional Geometry 6

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.
Plus One Maths Chapter Wise Previous Questions Chapter 12 Introduction to Three Dimensional Geometry 7

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
Plus One Maths Chapter Wise Previous Questions Chapter 12 Introduction to Three Dimensional Geometry 8
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:
Plus One Maths Chapter Wise Previous Questions Chapter 12 Introduction to Three Dimensional Geometry 9

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)
Plus One Maths Chapter Wise Previous Questions Chapter 12 Introduction to Three Dimensional Geometry 10

Question 9.
Find the centroid of the triangle with vertices (3,- 5,7), (- 1,7,- 6) and (1,1,2). (IMP-2010)
Answer:
Plus One Maths Chapter Wise Previous Questions Chapter 12 Introduction to Three Dimensional Geometry 11
= (1,1,1)

Question 10.
Show that the points (-2,3,5), (1,2,3) and (7,0,-1) are collinear. (IMP-2014)
Answer:
Plus One Maths Chapter Wise Previous Questions Chapter 12 Introduction to Three Dimensional Geometry 12

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:
Plus One Maths Chapter Wise Previous Questions Chapter 12 Introduction to Three Dimensional Geometry 13

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
Plus One Maths Chapter Wise Previous Questions Chapter 12 Introduction to Three Dimensional Geometry 14

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 Chapter Wise Previous Questions Chapter 12 Introduction to Three Dimensional Geometry 15

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:
Plus One Maths Chapter Wise Previous Questions Chapter 12 Introduction to Three Dimensional Geometry 16

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
Plus One Maths Chapter Wise Previous Questions Chapter 12 Introduction to Three Dimensional Geometry 17

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:
Plus One Maths Chapter Wise Previous Questions Chapter 12 Introduction to Three Dimensional Geometry 18

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:
Plus One Maths Chapter Wise Previous Questions Chapter 12 Introduction to Three Dimensional Geometry 19
Plus One Maths Chapter Wise Previous Questions Chapter 12 Introduction to Three Dimensional Geometry 20
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
Plus One Maths Chapter Wise Previous Questions Chapter 12 Introduction to Three Dimensional Geometry 17

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 Chapter Wise Previous Questions Chapter 12 Introduction to Three Dimensional Geometry 21

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 Chapter 12 Introduction to Three Dimensional Geometry 23

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