In This Post we are providing Chapter-12 Introduction to Three Dimensional Geometry NCERT MCQ for Class 11 Math which will be beneficial for students. These solutions are updated according to 2021-22 syllabus. These MCQS can be really helpful in the preparation of Board exams and will provide you with a brief knowledge of the chapter.
NCERT MCQ ON INTRODUCTION TO THREE DIMENSIONAL GEOMETRY
Question 1. The coordinates of a point which is equidistant from the points (0, 0, 0), (a, 0, 0), (0, b, 0), (0, 0, c) are given by
(a) (a/2 , b/2 , c/2,)
(b) ( -a/2 , -b/2 , c/2,)
(c) (a/2 , -b/2 , c/2,)
(d) (-a/2 , b/2 , c/2,)
Answer : A
Question 2. If x2+y2 = 1, then the distance from the point (x, y, 1-x2-y2 ) to the origin is
(a) 1
(b) – 1
(c) 0
(d) 2
Answer : A
Question 3. Three vertices of a parallelogram ABCD are A(1, 2, 3), B(-1, -2, -1) and C(2, 3, 2). Find the fourth vertex D.
(a) (– 4, – 7, – 6)
(b) (4, 7, 6)
(c) (4, 7, – 6)
(d) None of these
Answer : B
Question 4. If a parallelopiped is formed by planes drawn through the points (5, 8, 10) and (3, 6, 8) parallel to the coordinate planes, then the length of diagonal of the parallelopiped is
(a)2 √3
(b)3√2
(c) √2
(d) √3
Answer : A
Question 5. The points (5, – 4, 2),(4,– 3, 1), (7, -6, 4) and (8, – 7, 5) are the vertices of
(a) a rectangle
(b) a square
(c) a parallelogram
(d) None of these
Answer : C
Question 6. If the coordinates of the vertices of a ΔABC are A(-1, 3, 2), B(2, 3, 5) and C(3, 5, – 2), then ? ∠A is equal to
(a) 45°
(b) 60°
(c) 90°
(d) 30°
Answer : A
Question 7. Find the ratio in which the YZ-plane divides the line segment formed by joining the points (– 2, 4, 7) and (3, – 5, 8).
(a) externally 2 : 3
(b) internally 2 : 3
(c) internally 3 : 2
(d) externally 3 : 2
Answer : B
Question 8. Find the coordinates of the point which divides the line segment joining the points (– 2, 3, 5) and (1, -4, 6) in the ratio 2 : 3 externally.
(a) (– 8, – 17, 3)
(b) (– 8, 17, 3)
(c) (8, – 17, 3)
(d) None of these
Answer : B
Question 9. Find the length of the medians of the triangle with vertices A(0, 0, 6), B(0, 4, 0) and C(6, 0, 0).
(a) 7, 7, √34
(b) 7, 8, √34
(c) 7, 9, √34
(d) None of these
Answer : A
Question 10. Find the coordinates of the points which trisect the line segment joining the points P(4 , 2, -6) and Q(10, -16, 6).
(a) (6, – 4, – 2), (8, – 10, 2)
(b) (6, 4, – 2), (8, – 10, 2)
(c) (6, – 4, – 2), (8, 10, 2)
(d) None of these
Answer : B
Question 11. Find the centroid of a triangle, the mid-point of whose sides are D(1, 2, -3), E(3, 0, 1) and F (-1, 1, -4).
(a) (1, 1, 2)
(b) (1, 1, – 2)
(c) (– 1, –1, –2)
(d) (1, –1, –2)
Answer : B
Question 12. The points A(5, -1, 1), B(7, -4, 7), C(1, -6, 10) and D(-1, -3, 4) are vertices of a
(a) square
(b) rhombus
(c) rectangle
(d) None of these
Answer : B
Question 13. If vertices of a triangle are A(1, -1, 2), B(2, 0, -1) and C(0, 2, 1), then the area of a triangle is (a) √6
(b) 2√6
(c) 3√6
(d) 4√6
Answer : B
Question 14. The point ( -2, -3, -4) lies in the
(a) first octant
(b) seventh octant
(c) second octant
(d) eight octant
Answer : B
Question 15. The mid-points of the sides of a triangle are (5, 7, 11), (0, 8, 5) and (2, 3, – 1). Then, the vertices are
(a) (7, 2, 5), (3, 12, 17), (– 3, 4, – 7)
(b) (7, 2, 5), (3, 12, 17), ( 3, 4, 7)
(c) (7, 2, 5), (– 3, 12, 17), (– 3, – 4, – 7)
(d) None of the above
Answer : A
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