BITSAT Mathematics Three Dimensional Geometry MCQs

Question: A line segment has length 63 and direction ratios are 3, –2, 6. If the line makes an obtuse angle with x–axis, the components of the line vector are

• a) 27, – 18, 54
• b) – 27, 18, 54
• c) – 27, 18, –54
• d) 27, – 18, – 54

Answer: – 27, 18, –54

Question: The line,intersects the curve xy = c², z = 0 if c is equal to

• a) 

  

• b)

  

• c) 
• d) None of these

Answer:

Question: The angle between two planes is equal to

• a) The angle between the tangents to them from any point
• b) The angle between the normals to them from any point
• c) The angle between the lines parallel to the planes from any point
• d) None of these

Answer: The angle between the normals to them from any point

Question: What is the angle between the lines 

• a)

  

• b)

  

• c)

  

• d) None of these

Answer:

Question: Find the direction cosines of the line joining the points A(6, –7, –1) and B (2, –3, 1).

• a)

  

• b)

  

• c)

  

• d)

  

Answer:

Question: Find the equation of the line 3x – 6y – 2z – 15 = 2x + y – 2z + 5= 0 in parametric form.

• a)

  

• b)

  

• c)

  

• d)

  

Answer:

Question: The point of intersection of the lines andis

• a)

  

• b)

  

• c)

  

• d) None of these

Answer:

Question: The equation of line of intersection of planes 4x + 4y – 5z = 12, 8x + 12y – 13z = 32 can be written as

• a)

  

• b)

  

• c)

  

• d)

  

Answer:

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

• a) 3 : 5
• b) 5 : 7
• c) 1 : 3
• d) 4 : 5

Answer: 5 : 7

Question: Two lines L₁ : x 5, are coplanar. Then, a can take value (s)

• a) 1, 4, 5
• b) 1, 2, 5
• c) 3, 4, 5
• d) 2, 4, 5

Answer: 1, 4, 5

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

• a) 3 : 5
• b) 5 : 7
• c) 1 : 3
• d) 4 : 5

Answer: 5 : 7

Question: If the line through the points A (k, 1, –1) and B (2k, 0, 2) is perpendicular to the line through the points B and C (2 + 2k , k, 1), then what is the value of k?

• a) –1
• b) 1
• c) –3
• d) 3

Answer: 3

Question: Two lines L₁ : x 5, are coplanar. Then, a can take value (s)

• a) 1, 4, 5
• b) 1, 2, 5
• c) 3, 4, 5
• d) 2, 4, 5

Answer: 1, 4, 5

Question: A line makes the same angle θ with each of the X and Z-axes. If the angle β, which it makes with Y-axis, is such that sin² β = 3sin² θ, then cos² θequals

• a) 2/5
• b) 1/5
• c) 3/5
• d) 2/3

Answer: 3/5

Question: Find the angle between the lineand the plane 10x + 2y – 11z = 3.

• a)

  

• b)

  

• c)

  

• d)

  

Answer:

Question: The equation of the right bisector plane of the segment joining (2, 3, 4) and (6, 7, 8) is

• a) x + y + z + 15 = 0
• b) x + y + z – 15 = 0
• c) x – y + z – 15 = 0
• d) None of these

Answer: x + y + z – 15 = 0

Question: The coordinates of the point where the line through the points A (3, 4, 1) and B (5, 1, 6) crosses the XY - plane are

• a)

  

• b)

  

• c)

  

• d)

  

Answer:

Question: Find the angle between the two planes 2x + y – 2z = 5 and 3x – 6y – 2z = 7

• a) cos^–1 (4/21)
• b) cos^–1 (2/21)
• c) cos^–1 (1/21)
• d) cos^–1 (5/21)

Answer: cos^–1 (4/21)

Question: What is the value of n so that the angle between the lines having direction ratios (1, 1, 1) and (1, –1, n) is 60°?

• a) √3
• b) √6
• c) 3
• d) None of these

Answer: √6

Question: The foot of the perpendicular from the point (7, 14, 5) to the plane 2x + 4y – z = 2 are

• a) (1, 2, 8)
• b) (3, 2, 8)
• c) (5, 10, 6)
• d) (9, 18, 4)

Answer: (1, 2, 8)

Question: Find the coordinates of the point where the line joining the points (2, –3, 1) and (3, – 4, – 5) cuts the plane 2x + y + z = 7.

• a) (1, 2, – 7)
• b) (1, – 2, 7)
• c) (–1, – 2, 7)
• d) (1, 2, 7)

Answer: (1, – 2, 7)

Question: Gives the line L : and the plane π : x – 2y – z = 0. Of the following assertions, the only one that is always true is

• a)

   

• b) L lies in π
• c) L is not parallel to π
• d) None of these

Answer: L lies in π

Question: The perpendicular distance of P(1, 2, 3) from the line is

• a) 7
• b) 5
• c) 0
• d) 6

Answer: 7

Question: The equation of the plane containing the line is a (x – x₁) + b (y – y₁) + c (z – z₁) = 0. Correct option is

• a) ax₁ + by₁ + cz₁ = 0
• b) al + bm + cn = 0
• c)

  

• d) lx₁ + my₁ + nz₁ = 0

Answer: al + bm + cn = 0

Question: If the line  lies in the plane 2x – 4y + z = 7, then the value of k is

• a) 4
• b) -7
• c) 7
• d) No real value

Answer: 7