BITSAT Mathematics Vector Algebra MCQs

Question: If the position vectors of the vertices A, B, C of a triangle ABC are and respectively, the triangle is

• a) Equilateral
• b) Isosceles
• c) Scalene
• d) Right angled and isosceles also

Answer: Right angled and isosceles also

Question: For unit vectors b and c and any non-zero vector a, the value of {(a + b) × (a + c)} × (b + c)}. (b + c) is

• a) | a |²
• b) 2 | a |²
• c) 3 | a |²
• d) None of these

Answer: None of these

Question: If θ be the angle between vectors a = i + 2j + 3k and b = 3i + 2j + k, then cos θ equals

• a) 5/7
• b) 6/7
• c) 4/7
• d) 1/2

Answer: 5/7

Question: Find the angle between the vectors

• a) 15°
• b) 45°
• c) 35°
• d) 60°

Answer: 60°

Question: If are non-coplanar vectors and λ is a real number, then the vectorsare non coplanar for

• a) No value of λ 
• b) All except one value of λ
• c) All except two values of λ
• d) All values of λ

Answer: All except two values of λ

Question: A vector of magnitude 5 and perpendicular to is

• a)

   

• b)

  

• c)

  

• d)

  

Answer:

Question: i × ( j × k ) + j × ( k × i ) + k ( i × j ) equals

• a) i
• b) j
• c) k
• d) 0

Answer: 0

Question: What is the vector joining the points (3, 1, 14) and (–2, –1, –6) ?

• a)

  

• b)

  

• c)

  

• d)

  

Answer:

Question: If = 676 and  then is equal to

• a) 13
• b) 26
• c) 39
• d) None of these

Answer: 13

Question: Which one of the following is the unit vector perpendicular to both and?

• a)

  

• b)

  

• c)

  

• d)

  

Answer:

Question: Let  be non-coplanar unit vectors equally inclined to one another at an acute angle q. Then in terms of θis equal to

• a)

  

• b)

  

• c)

  

• d) None of these

Answer:

Question: The dot product of a vector with the vectors are 0, 5 and 8 respectively. The vector is

• a)

  

• b)

  

• c)

  

• d)

  

Answer:

Question: Let a, b and c be three vectors satisfying a × b = (a ×c), |a| = |c| = 1, |b| = 4 and |b × c| = √15 . If b – 2c = λa, then λ equals

• a) 1
• b) -1
• c) 2
• d) -4

Answer: -4

Question: If the middle points of sides BC, CA & AB of triangle ABC are respectively D, E, F then position vector of centre of triangle DEF, when position vector of A, B, C are respectively  is

• a)

  

• b)

  

• c)

  

• d)

  

Answer:

Question: The angle between any two diagonal of a cube is

• a) 45°
• b) 60°
• c) 30°
• d) tan^-1(2 √2)

Answer: tan^-1(2 √2)

Question: If are three unit vectors such that where  is null vector, then  is

• a) -3
• b) -2
• c) 

  

• d) 0

Answer:

Question: If are three non-coplanar vectors, then the value of  is

• a) 0
• b) 2
• c) 1
• d) None of these

Answer: 0

Question: If vectors 2i – j + k, i + 2j – 3k and 3i + aj + 5k are coplanar, then the value of a is

• a) 2
• b) -2
• c) -1
• d) -4

Answer: -4

Question: The unit vector perpendicular to the vectors  is

• a)

  

• b)

  

• c)

  

• d)

  

Answer:

Question: If a.b = a.c and a × b = a × c, then correct statement is

• a) a || (b – c)
• b)

  

• c) a = 0 or b = c
• d) None of these

Answer: a = 0 or b = c

Question: Two vectors  and are such that |+ | = |-| The angle between the two vectors will be–

• a) 60°
• b) 90°
• c) 180°
• d) 0°

Answer: 90°

Question: If = 676 and  then is equal to

• a) 13
• b) 26
• c) 39
• d) None of these

Answer: 13

Question: Which one of the following is the unit vector perpendicular to both and?

• a)

  

• b)

  

• c)

  

• d)

  

Answer:

Question: With respect to a rectangular cartesian coordinate system, three vectors are expressed as : andwhereare unit vectors, along the X, Y and Zaxis respectively. The unit vectoralong the direction of sum of these vector is –

• a)

  

• b)

  

• c)

  

• d)

  

Answer:

Question: If the middle points of sides BC, CA & AB of triangle ABC are respectively D, E, F then position vector of centre of triangle DEF, when position vector of A, B, C are respectively i + j, j + k, k + i is –

• a) (1/3) (i + j + k)
• b) (i + j + k)
• c) 2 (i + j + k)
• d) (2/3) (i + j + k)

Answer: (2/3) (i + j + k)