JEE Mathematics Vector Algebra MCQs

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: A

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: A

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: A

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: A

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: A

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: A

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: A

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

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: A

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

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

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: A

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: A

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: A