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:

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

(x_{1}, y_{1}, z_{1}) ; (x_{1}, y_{1}, z_{1})and(x_{1}, y_{1}, z_{1}) (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: