# MCQ Questions for Class 11 Introduction to Three Dimensional Geometry with Answers

Students can refer to the following MCQ Questions for Class 11 Introduction to Three Dimensional Geometry with Answers provided below based on the latest curriculum and examination pattern issued by CBSE and NCERT. Our teachers have provided here a collection of multiple choice questions for Introduction to Three Dimensional Geometry Class 11 covering all topics in your textbook so that students can assess themselves on all important topics and thoroughly prepare for their exams

## Class 11 Introduction to Three Dimensional Geometry MCQs Questions with Answers

We have provided below MCQs questions for Class 11 Introduction to Three Dimensional Geometry with answers which will help the students to go through the entire syllabus and practice multiple choice questions provided here with solutions. As Introduction to Three Dimensional Geometry MCQs in Class 11 Mathematics pdf download can be really scoring for students, you should go through all problems provided below so that you are able to get more marks in your exams.

Question. P(a, b, c); Q (a + 2, b + 2, c – 2) and R (a + 6, b + 6, c – 6) are collinear. Consider the following statements :
1. R divides PQ internally in the ratio 3 : 2
2. R divides PQ externally in the ratio 3 : 2
3. Q divides PR internally in the ratio 1 : 2
Which of the statements given above is/are correct ?
(a) 1 only
(b) 2 only
(c) 1 and 3
(d) 2 and 3

D

Question: A plane is parallel xy-plane, so it is perpendicular to
(a) z-axis
(b) y-axis
(c) x-axis
(d) None of these

A

Question: The point ( -2,3,-4) lies in the
(a) first octant
(b) seventh octant
(c) second octant
(d) eight octant

B

Question: The distance of point P(3, 4,5)  from the yz-plane is
(a) 3 units
(b) 4 units
(c)5 units
(d) 550 units

A

Question: The locus of a point for which y = 0, z = 0 is
(a) equation of x-axis
(b) equation of y-axis
(c) equation of z-axis
(d) None of these

A

Question: L is the foot of the perpendicular drawn from a point P( (3,4,5) on the xy-plane. The coordinates of point L are
(a) (3, 0, 0)
(b) (0, 4, 5)
(c) (3, 0, 5)
(d) None of these

D

Question: What is the length of foot of perpendicular drawn from the point P(3 ,4 ,5)  on y-axis?
(a) √41
(b) √34
(c) 5
(d) None of these

B

Question: If A and B be the points (3, 4, 5) and (– 1, 3, – 7) respectively, find the equation of the set of points P such that(PA)2+ (PB)2=k2 , where K is a constant.
(a) 2(x2+y2+z2) +4x+14y+az+109-k2=0
(b) 2(x2+y2+z2)-4x-14y+AZ+109-k2=0
(c ) x2+y2+z2+4x+14y+az+109-k2=0
(d) None of the above

B

Question: If the distance between the points ( a,01,) and (0,1,2) )  is √27, then the value of a is
(a) 5
(b) ± 5
(c) – 5
(d) None of these

B

Question: If x-coordinate of a point P of line joining the points Q( 2, 2, 1) and R( 5,2 ,2)  is 4, then the z-coordinate of P is
(a) –2
(b) –1
(c) 1
(d) 2

B

Question: Distance of the point (1, 2, 3) from the coordinate axes are
(a) 13,10, 5
(b) √13 √10 √5
(c) √5 √13 √10
(d) 1/√13,1/√10,1/√5

B

Question: 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/1,b/2,c/2)
(c) (a/2,-b/2,c/2)
(d) (-a/2,b/2,c/2)

A

Question: If the sum of the squares of the distance of a point from the three coordinate axes be 36, then its distance from the origin is
(a) 6
(b) 2√2
(c) 2√3
(d) None of these

B

Question: If x2+y2=1,then the distance from the point ((xy,√1-x2-y2)  to the origin is
(a) 1
(b) – 1
(c) 0
(d) 2

A

Question: Three vertices of a parallelogram ABCD are A (1,2, 3)B (-1,-2,-1) 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

A

Question: If the sum of the squares of the distance of a point from the three coordinate axes be 36, then its distance from the origin is
(a) 6
(b) 2√2
(c) 2√3
(d) None of these

B

Question: 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

B

Question: 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

A

Question: 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

B

Question: 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

A

Question: 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

C

Question: 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

A

Question: The points  A(5,1,) 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

B

Question: 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)

B

Question. The point equidistant from the four points (0,0, 0), (3/2, 0, 0), (0,5/2, 0) and (0, 0, 7/2) is:
(a) (2/3 , 1/3 , 2/5)
(b) (3, 2, 3/5)
(c) (3/4 , 5/4 , 7/4)
(d) (1,0, 1/2)

C

Question. For every point P(x, y, z) on the xy-plane,
(a) x = 0
(b) y = 0
(c) z = 0
(d) none of these

C

Question. Find the equation of set points P such that PA2 + PB2 = 2K2, where A and B are the points (3, 4, 5) and (–1, 3, –7), respectively :
(a) K2 – 109
(b) 2K 2 – 109
(c) 3K2 – 109
(d) 4K 2 – 10

B

Question. The distance of the point P(a, b, c) from the x-axis is
(a) (b2 + c2)
(b) (a2 + c2)
(c) (a2 + b2)
(d) none of these

A

Question. The ratio in which the join of ( 2, 1, 5) and (3, 4, 3) is divided by the plane (x + y – z)=1/2/is:
(a) 3 : 5
(b) 5 : 7
(c) 1 : 3
(d) 4 : 5

B

Question. For every point P(x, y, z) on the x-axis (except the origin),
(a) x = 0, y = 0, z ≠ 0
(b) x = 0, z = 0, y ≠ 0
(c) y = 0, z = 0, x ≠ 0
(d) none of these

C

Question. Point (–3, 1, 2) lies in
(a) Octant I
(b) Octant II
(c) Octant III
(d) Octant IV

B

Question. ABC is a triangle and AD is the median. If the coordinates of A are ( 4, 7, – 8)and the coordinates of centroid of the triangle ABC are (1, 1, 1), what are the coordinates of D?
(a) (– 1/2 ,2,11)
(b)(– 1/2 , –2, 11/2)
(c) (–1, 2, 11)
(d) (–5, –11, 19)

B

Question. The three vertices of a parallelogram taken in order are (–1, 0), (3, 1) and (2, 2) respectively. Find the coordinate of the fourth vertex.
(a) (2,1)
(b) (–2,1)
(c) (1,2)
(d) (1,–2)

B

Question. If the sum of the squares of the distance of the point ( x, y, z) from the points ( a, 0, 0) and ( –a , 0, 0) is 2c2, then which one of the following is correct?
(a) x2 + a2 = 2c2 – y2 – z2
(b) x2 + a2 = c2 – y2 – z2
(c) x2 – a2 = c2 – y2 – z2
(d) x2 + a2 = c2 + y2 + z2

B

Question. What is the perpendicular distance of the point P(6, 7, 8) from xy-plane?
(a) 8
(b) 7
(c) 6
(d) none of thes

A

Question. What is the locus of a point which is equidistant from the points (1, 2, 3) and (3, 2, – 1) ?
(a) x + z = 0
(b) x – 3z = 0
(c) x – z = 0
(d) x – 2z = 0

D

Question. The point equidistant from the four points (0,0, 0), (3/2, 0, 0), (0,5/2, 0) and (0, 0, 7/2) is:
(a) (2/3 , 1/3 , 2/5)
(b) (3, 2, 3/5)
(c) (3/4 , 5/4 , 7/4)
(d) (1/2,0, -1)

C

Question. What is the shortest distance of the point (1, 2, 3) from x- axis ?
(a) 1
(b) 6
(c) 13
(d) 14

C

Question. What are coordinates of the point equidistant from the points (a, 0, 0), (0, a, 0), (0, 0, a) and (0, 0, 0) ?
(a) (a/3 , a/3 , a/3)
(b) (a/2 , a/2 , a/2)
(c) (a, a, a)
(d) (2a, 2a, 2a)

B

Question. The equation of locus of a point whose distance from the y-axis is equal to its distance from the point (2, 1, –1) is
(a) x2 + y2 + z2 = 6
(b) x2 – 4x + 2z + 6 = 0
(c) y2 – 2y – 4x + 2z + 6 = 0
(d) x2 + y2 – z2 = 0

C

Question. The ratio in which the join of points (1, –2, 3) and (4, 2, –1) is divided by XOY plane is
(a) 1 : 3
(b) 3 : 1
(c) –1 : 3
(d) None of these

B

Question. L is the foot of the perpendicular drawn from a point (6, 7, 8) on x-axis. The coordinates of L are
(a) (6, 0, 0)
(b) (0, 7, 0)
(c) (0, 0, 8)
(d) none of these

A

Question. The points (5, 2, 4), (6, –1, 2) and (8, –7, k) are collinear if k is equal to
(a) –2
(b) 2
(c) 3
(d) –1

A

Question. In three dimensional space the path of a point whose distance from the x-axis is 3 times its distance from the yz-plane is:
(a) y2 + z2 = 9x2
(b) x2 + y2 =3z2
(c) x2 + z2 = 3y2
(d) y2 – z2 = 9x2

A

Question. What is the ratio in which the line joining the points (2,4, 5) and (3, 5, – 4) is internally divided by the xy-plane?
(a) 5 : 4
(b) 3 : 4
(c) 1 : 2
(d) 7 : 5

A

Question. L is the foot of the perpendicular drawn from a point P(6, 7, 8) on the xy-plane. What are the coordinates of point L?
(a) (6, 0, 0)
(b) (6, 7, 0)
(c) (6, 0, 8)
(d) none of these