JEE Mathematics Vector Algebra MCQs

Question:

• a)

  

• b)

  

• c)

  

• d) None of these

Answer:

Question: p = 2a – 3b, q = a – 2b + c, r = – 3a + b + 2c; where a, b and c being non-zero, non-coplanar vectors, then the vector –2a + 3b – c is equal to

• a) -7q+r/5
• b) 4p - 2r
• c) p - 4q
• d) 2p - 3q + r

Answer: -7q+r/5

Question: P is the point of intersection of the diagonals of the parallelogram ABCD. If O is any point, then

• a)

  

• b)

  

• c)

  

• d)

  

Answer:

Question:

• a)

  

• b)

  

• c)

  

• d)

  

Answer:

Question:

• a)

  

• b)

  

• c)

  

• d)

  

Answer:

Question:

• a) 8d.(a + b + c)
• b) 8d×(a + b + c)
• c)

  

• d)

  

Answer: 8d.(a + b + c)

Question: A force of magnitude 5 units acting along the vector 2i - 2j + k displaces the point of application from (1, 2, 3) to (5, 3, 7), then the work done is

• a) 50/3
• b) 50/7
• c) 25/3
• d) 25/4

Answer: 50/3

Question: If a = i + j + k, b = i + 3j + 5k and c = 7i + 9j +11k , then the area of the parallelogram having diagonals a + b and b + c is

• a) 4√6
• b) √6
• c) √6/2
• d) None of these

Answer: 4√6

Question:

• a)

  

• b)

  

• c)

  

Answer:

Question: A unit vector perpendicular to the plane containing the vectors i – j + k and –i + j + k is

• a) i + j/√2
• b) j– k/√2
• c) i – j/√2
• d) None of these

Answer: i + j/√2

Question:

• a)

  

• b) sin Θ
• c) 2 sin Θ
• d) sin 2Θ

Answer: 

Question:

• a) 3√6 sq. units
• b) 13√2 sq. units
• c) 15√3 sq. units
• d) √13 sq. units

Answer: 3√6 sq. units

Question:

• a) √14
• b) √17
• c) √41
• d) √7

Answer: √14

Question:

• a)

  

• b)

  

• c)

  

• d)

  

Answer:

Question:

• a) 16
• b) none
• c) 48
• d) Both

Answer: 16

More Questions..............................

Question:

• a) 0, – 1
• b) none of these
• c) 0, 1
• d) 1, – 1

Answer: 0, – 1

Question:

• a)

  

• b)

  

• c)

  

• d)

  

Answer:

Question:

• a)

  

• b)

  

• c)

  

• d)

  

Answer:

Question:

• a) 7/3
• b) 3/7
• c) 3
• d) 7

Answer: 7/3

Question: If the difference of two unit vectors is also a unit vector, then the angle between them is :

• a)

  

• b)

  

• c)

  

• d)

  

Answer:

Question:

• a)

  

• b)

  

• c) 0
• d) 1

Answer:

Question:

(1) 1 (2) √3
(3) 0 (4) 2

• a) 2 and 4 are correct
• b) 1, 2 and 3 are correct
• c) 1 and 2 are correct
• d) 1 and 3 are correct

Answer: 2 and 4 are correct

Question:

• a) 1, 2 and 3 are correct
• b) 1 and 2 are correct
• c) 2 and 4 are correct
• d) 1 and 3 are correct

Answer: 1, 2 and 3 are correct

Question: Let a and b be two non-collinear unit vectors. If u = a - (a . b) b and v = a × b, then | v | is

(1) | u |                 (2) | u | + | u . a |
(3) | u | + | u . b | (4) | u | + u.(a + b)

• a) 1 and 3 are correct
• b) 1 and 2 are correct
• c) 1, 2 and 3 are correct
• d) 2 and 4 are correct

Answer: 1 and 3 are correct

Question:

• a)

  

• b)

  

• c)

  

• d)

  

Answer:

Question:

• a) None
• b)

  

• c)

  

• d)

  

Answer: None

Question:

• a) 8/5
• b) 5/8
• c) 0
• d) 1

Answer: 8/5

Question:

• a) Statement -1 is False, Statement-2 is True.
• b) Statement -1 is True, Statement-2 is False.
• c) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1.
• d) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.

Answer: Statement -1 is False, Statement-2 is True.

Question:

• a) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.
• b) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1.
• c) Statement -1 is False, Statement-2 is True.
• d) Statement -1 is True, Statement-2 is False.

Answer: Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.

Question:

• a) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1.
• b) Statement -1 is False, Statement-2 is True.
• c) Statement -1 is True, Statement-2 is False.
• d) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.

Answer: Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1.

Question: If a, b, c are any three vectors and their inverse are a^-1,b^-1,c^-1and [a b c ] ≠ 0, then [a^-1b^-1c^-1] will be

• a) Non–Zero
• b) Zero
• c) One
• d) [a b c ]

Answer: Non–Zero

Question: If a, b, c are non–coplanar vectors and d = λa + μb + vc then λ is equal to

• a)

  

• b)

  

• c)

  

• d)

  

Answer:

Question: Vector coplanar with vectors i + j and j + k and parallel to the vector 2i – 2j – 4k, is

• a) i + j – k
• b) i – k
• c) i – j – 2k
• d) 3i + 3j – 6k

Answer: i + j – k

Question: (a + b). [(b + c) × (a + b + c)] =

• a) [a b c]
• b) 2[a b c]
• c) – [a b c]
• d) 0

Answer: [a b c]

Question: Given the following equations for vectors x and y x + y = a ..... (i) x × y = b ..... (ii) x . a = 1 ..... (iii) Then the values of x and y respectively are

• a) None of these
• b) a – b, b
• c) a, a – x
• d) b, a – b

Answer: None of these

Question: [b × c c × a a × b] is equal to

• a) [a b c]²
• b) a × (b × c)
• c) 2[a b c]
• d) [a b c]

Answer: [a b c]²

Question: a × [a × (a × b)] is equal to

• a) (a.a) (b × a)
• b) a. (b × a) – b. (a × b)
• c) (a × a). (b × a)
• d) [a. (a × b)] a

Answer: (a.a) (b × a)

Question: If a, b, c are three coplanar vectors, then [a + b b + c c + a]=

• a) 0
• b) 2 [a b c]
• c) [a b c]
• d) 3 [a b c]

Answer: 0

Question: Let a, b, c be three vectors from a × (b × c) = (a × b) × c, if

• a) b × (a × c) = 0
• b) c × a = a × b
• c) a (b × c) = 0
• d) c × b = b × a

Answer: b × (a × c) = 0

Question:

• a) 0
• b)

  

• c)

  

• d) none of these

Answer: 0

Question:

• a) b = 1, c = a
• b) a = 1, b = c
• c) a = 1, c = 1
• d) b = 2, c = 2a

Answer: b = 1, c = a

Question:

• a)

  

• b)

  

• c)

  

• d)

  

Answer:

Question:

• a) 0
• b) 2
• c) 13
• d) 1

Answer: 0

Question:

• a)

  

• b)

  

• c)

  

• d)

  

Answer:

Question:

• a)

  

• b)

  

• c)

  

• d)

  

Answer:

Question:

• a)

  

• b) 1
• c) –1
• d) 0

Answer:

Question:

• a)

  

• b)

  

• c)

  

• d)

  

Answer:

Question:

• a) 0
• b) 1
• c) 9
• d) None of these

Answer: 0

Question:

• a) no value of λ
• b) exactly three values of λ
• c) exactly two values of λ
• d) exactly one value of λ

Answer:  no value of λ

Question:

• a) neither x nor y
• b) only x
• c) only y
• d) both x and y

Answer: neither x nor y

Question: If the vectors (-bc,b² + bc, c² + bc) , (a² + ac, - ac, c² + ac) and (a² + ab, b² + ab, - ab) are coplanar, where none of a, b or c is zero, then

(1) bc + ca + ab = 0 (2) a² + b² + c² = (a + b + c)²
(3) a² + b² + c² = 1 (4) a + b + c = 0

• a) 1 and 2 are correct
• b) 2 and 4 are correct
• c) 1 and 3 are correct
• d) 1, 2 and 3 are correct

Answer: 1 and 2 are correct

Question: If the volume of parallelopiped whose adjacent edges are

(1) 9/2

(2) – 1

(3) 1

(4) 5/2

• a) 1 and 2 are correct
• b) 1 and 3 are correct
• c) 2 and 4 are correct
• d) 1, 2 and 3 are correct

Answer: 1 and 2 are correct

Question:

• a) 1, 2 and 3 are correct
• b) 1 and 2 are correct
• c) 1 and 3 are correct
• d) 2 and 4 are correct

Answer: 1, 2 and 3 are correct

Question:

• a) Statement -1 is True, Statement-2 is False.
• b) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.
• c) Statement -1 is False, Statement-2 is True.
• d) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1.

Answer: Statement -1 is True, Statement-2 is False.

Question:

• a) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.
• b) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1.
• c) Statement -1 is False, Statement-2 is True.
• d) Statement -1 is True, Statement-2 is False.

Answer: Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.

Question:

• a) Statement -1 is True, Statement-2 is False.
• b) Statement -1 is False, Statement-2 is True.
• c) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1.
• d) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.

Answer: Statement -1 is True, Statement-2 is False.