Read and download free pdf of CBSE Class 11 Mathematics Introduction To 3 Dimensional Geometry Worksheet. Students and teachers of Class 11 Mathematics can get free printable Worksheets for Class 11 Mathematics Chapter 12 Introduction of 3D in PDF format prepared as per the latest syllabus and examination pattern in your schools. Class 11 students should practice questions and answers given here for Mathematics in Class 11 which will help them to improve your knowledge of all important chapters and its topics. Students should also download free pdf of Class 11 Mathematics Worksheets prepared by teachers as per the latest Mathematics books and syllabus issued this academic year and solve important problems with solutions on daily basis to get more score in school exams and tests
Worksheet for Class 11 Mathematics Chapter 12 Introduction of 3D
Class 11 Mathematics students should refer to the following printable worksheet in Pdf for Chapter 12 Introduction of 3D in Class 11. This test paper with questions and answers for Class 11 will be very useful for exams and help you to score good marks
Class 11 Mathematics Worksheet for Chapter 12 Introduction of 3D
Q1. Find the ratio in which the line joining the points (2, 4, 16) and (3, 5, -4) is divided by the plane 2x – 3y+ z + 6 = 0. Also find the co-ordinates of the point of division.
Q2. Find the ratio in which the line segment joining the points (2, 4, 5) and (3, 5, -4) is divided by the YZplane. Also find the co-ordinate of the point of division.
Q3. Using section formula, show that point P (2, -3, 4), Q (-1, 2, 1) and R (0, 1/3, 2) are collinear.
Q4. Find the co-ordinates of the centroid of the triangle whose vertices are (1, 5, -2), (3, 2, 7) and (-7, -1, 4)
Q5. Three vertices of a parallelogram ABCD are A (3, -4, 7) B (5, 3, -2) and C (1, 2, -3). Find the fourth vertex D.
Q6. Find the coordinates of the points which trisect the line segment AB, given A (2, 1, -3) and B (5, -8, 3).
Q7. The x co-ordinate of a point is 9. Find its other co-ordinates if this point lies on the line joining the points (7, 2, 1) and (10, 5, 7)
Q8. A point P(x, y, z) is such that 3PA = 2PB, when A and B are the points (1, 3, 4) and (1, -2, -1) respectively. Find the equation to the locus of the point P.
Q9. Show that the points (-1, -6, 10), (1, -3, 4), (-5, -1, 1) and (-7, -4, 7) are the vertices of a rhombus.
Q10. Prove that the points (1, 2, 3), (-1, 1, 4) and (0, 3, 3) and (1, 3, 2) are equidistance from the pt. (-1, 1, 1).
Q11. Find the co-ordinates of the point which divides the line segment joining the points (-2, 3, 5) and (1, -4, -6) in the ratio (2:3 internally (ii) 2:3 externally
Q.1 Using section formula, prove that the three points (– 2, 3, 5), (1, 2, 3) and (7, 0, –1) are collinear.
Q.2 A point is on the x-axis. What is its y-coordinate and z-coordinate?
Q.3 Write the coordinates of the mid-point of the line segment joining two points P(x1, y1, z1) and Q(x2, y2, z2).
Q.4 Find the equation of set of points P such that PA2 + PB2 = 2k2, where A and B are the points (1, 2, 3) and (1, 0, 0), respectively.
Q.5 Prove that the points P(1, 2, 3), Q(–1, –1, –1) and R(3, 5, 7) are collinear. (2 marks)
Q.6 Find the coordinates of the point which divides externally the line segment joining the points (1, –2, 3) and (3, 4, –5) in the ratio 2 : 3.
Q.7 Find the image of (–2,3,4) in the yz- plane.
Q.8 Three vertices of a parallelogram ABCD are A(4, 0, 3), B (3, 4, – 2) and C (– 2, 0, 1). Find the coordinates of the fourth vertex.
Q.9 Find the point in XY-plane which is equidistant from three points A(2,0,3), B(0,3,2) and C(0,0,1).
Q.10 Name the octants in which the following points lie: (2, 3, 4), (1, –2, 6).
Q.11 Find the ratio in which the line joining the points (1, 2, 3) and (- 3, 4, - 5) is divided by the xy-plane. Also, find the coordinates of the point of division.
Q.12 A point P is at a distance of 6 units from the origin on the Z axis. Write the coordinates of P.
Q.13 Find centroid of a triangle, mid-points of whose sides are (1, 2, - 3), (2, 0, 1) and (- 1, 1, - 4).
Q.14 Find lengths of the medians of the triangle with vertices A (0, 0, 6), B (0, 4, 0) and (6, 0, 0).
Q.15 Find the ratio in which the YZ-plane divides the line segment formed by joining the points (-2,4,7) and (3,-5,8).
Q.16 Given that P (3, 2, –4), Q (5, 4, –6) and R (9, 8, –10) are collinear. Find the ratio in which Q divides PR. (2 marks)
Q.17 Write the coordinates of the centroid of triangle, whose vertices are P(x1, y1, z1), Q(x2, y2, z2) and R (x3, y3, z3).
Q.18 Are the points A(3, 6, 9), B(10, 20, 30) and C(25, -41, 5) the vertices of a right angles triangle?
Q.19 Find the distance between the points P(1, 0, 4) and Q (– 4, 1, 0).
Q.20 Find the locus of the point which is equidistant from the points A(0,2,3) and B(2,–2,1).
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Worksheet for CBSE Mathematics Class 11 Chapter 12 Introduction of 3D
We hope students liked the above worksheet for Chapter 12 Introduction of 3D designed as per the latest syllabus for Class 11 Mathematics released by CBSE. Students of Class 11 should download in Pdf format and practice the questions and solutions given in the above worksheet for Class 11 Mathematics on a daily basis. All the latest worksheets with answers have been developed for Mathematics by referring to the most important and regularly asked topics that the students should learn and practice to get better scores in their class tests and examinations. Expert teachers of studiestoday have referred to the NCERT book for Class 11 Mathematics to develop the Mathematics Class 11 worksheet. After solving the questions given in the worksheet which have been developed as per the latest course books also refer to the NCERT solutions for Class 11 Mathematics designed by our teachers. We have also provided a lot of MCQ questions for Class 11 Mathematics in the worksheet so that you can solve questions relating to all topics given in each chapter.
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