Class 11 Mathematics Introduction To Three-Dimensional Geometry MCQs

Question.  If orthocentre and circumcentre of a triangle are respectively (1, 1, 1) and (3, 2, 2), then the coordinates of its centroid is 
(a) (-7/3 , 5/3 , 5/3,)
(b)  (7/3 , 5/3 , 5/3,)
(c)  (5/3 , 7/3  , 5/3)
(d) None of these

Answer :   B

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

Answer :   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

Answer :   A

Question. If the vertices of a triangle are A(0, 4, 1), B(2, 3, -1) and C(4, 5, 0), then orthocentre of a ΔABC is  
(a) (4, 5, 0)
(b) (2, 3, – 1)
(c) (– 2, 3, – 1)
(d) None of the above

Answer :   B

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

Answer :   A

Question. The point A(1, -1, 3), B(2, -4, 5) and C(5, -13, 11) are 
(a) collinear
(b) non-collinear
(c) Do not say anything
(d) None of these

Answer :   A

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

Answer :   A

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

Answer :   B

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

Answer :   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

Answer :   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 =0 , where K is a constant. 
(a) 2(X2+Y2+Z2)+4X+14Y+4Z+109-K2=0
(b) 2(X2+Y2+Z2)-4X-14Y+4Z+109-K2=0
(c) X2+Y2+Z2+4X+14Y+4Z109-K2=0
(d) None of the above

Answer :   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

Answer :   B

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)3√2
(c)2√3
(d) None of these

Answer :   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/2 , -b/2 , c/2,)
(c)  (a/2 , -b/2 , c/2,)
(d) (-a/2 , b/2 , c/2,)

Answer :   A

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

Answer :   B

Question. 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

Question. The area of the triangle, whose vertices are at the points (2, 1, 1), (3, 1, 2) and (– 4, 0, 1) is 
(a) √19
(b) 1/2√19
(c)1/2√38
(d)1/2√57

Answer :   C

Question. The triangle formed by the points (0, 7, 10), (-1, 6, 6), (-4, 9, 6) is 
(a) equilateral
(b) isosceles
(c) right angled
(d) right angled isosceles

Answer :   D

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

Answer :   D