CBSE Class 12 Mathematics Vectors Algebra MCQs Set D

Question. The perpendicular distance of A(1, 4, –2) from BC, where coordinates of B and C are respectively (2, 1, –2) and (0, –5, 1) is
(a) 3/7
(b) √26/7
(c) 3/√26/7
(d) √26
Answer: c

Question. Which of the following is an example of two different vectors with same magnitude?
(a) (2î +3ĵ + k̂) and (2î +3ĵ - k̂)
(b) (3î + 5ĵ + k̂) and (3î + 4ĵ + k̂)
(c) (ĵ + k̂) and (2ĵ + 3k̂)
(d) None of the above
Answer: a

Question. ABCD be a parallelogram and M be the point of intersection of the diagonals, if O is any point, then OA + OB + OC + OD is equal to
(a) 3 OM
(b) 2 OM
(c) 4 OM
(d) OM
Answer: c

Question. Let a̅ , b̅ , c̅ be three vectors of magnitudes 3, 4 and 5 respectively. If each one is perpendicular to the sum of the other two vectors, then | a̅ + b̅ + c̅ | =
(a) 5
(b) 3 √2
(c) 5 √2
(d) 12
Answer: c

Question. If position vector of a point A is a̅ + 2b̅ and any point P(a̅) divides A̅B̅ in the ratio of 2 : 3, then position vector of B is
(a) 2 a̅ -b̅
(b) b̅ - 2a̅
(c) a̅ -3b̅
(d) b̅
Answer: c

Question. Which of the following is true?
(a) î.î = ĵ.ĵ = k̂.k̂ = 0
(b) î.ĵ = ĵ.k̂= k̂.î = 0
(c) Both (a) and (b) are true
(d) Both (a) and (b) are not true
Answer: d

Question. Multiplication of two vectors is defined in two ways, namely
(a) scalar product and dot product
(b) vector product and cross product
(c) scalar product and vector product
(d) None of the above
Answer: c

Question. Consider points A, B, C and D with position vectors 7î - 4ĵ + 7k̂ , î - 6ĵ + 10k̂ , -î - 3ĵ + 4k̂ and 5î - ĵ + 5k̂ respectively. Then ABCD is a
(a) parallelogram but not a rhombus
(b) square
(c) rhombus
(d) None of these
Answer: d

Question. The three vectors î + ĵ , ĵ + k̂ , k̂+ î taken two at a time form three planes. The three unit vectors drawn perpendicular to these three planes form a parallelopiped of volume :
(a) 1/3
(b) 4
(c) 3√3/4
(d) 4/3√3
Answer: d

Question. If a = 2î + ĵ + 3k̂ , b = -î + 2ĵ + k̂ and c = 3î + ĵ + 2k̂ then a.(b × c) is equal to
(a) – 15
(b) 15
(c) – 10
(d) – 5
Answer: c

Question. Which of the following statement is correct?
(a) a.(b x c) = [b c a]
(b) [a b c] = [c a b]
(c) [c a b] = c.(a x b) = (a x b).c
(d) All are correct
Answer: d

Question. Which of the following is correct?
(a) [a b c] = [a c b]
(b) [a c b] = 0
(c) Both (a) and (b) are correct
(d) Both (a) and (b) are incorrect
Answer: a

Question. If θ is the angle between any two vectors a and b, then |a.b| = a x b| , where θ is equal to
(a) zero
(b) π/4
(c) π/2
(d) π
Answer: b

Question. If a̅ , b̅, c̅ are mutually perpendicular unit-vector, then |a̅ + b̅ + c̅| equals :
(a) 1
(b) √2
(c) √3
(d) 2
Answer: c

Question. If |a̅ | = 3, |b̅ | = 4 , then a value of λ for which a̅ + λ b̅ is perpendicular to a̅ - λb̅ is :
(a) 9/16
(b) 3/4
(c) 3/2
(d) 4/3
Answer: b

Question. Which one of the following statement is not correct ?
(a) Vector product is commutative
(b) Vector product is not associative
(c) Vector product is distributive over addition
(d) Scalar product is commutative
Answer: a

Question. ABCDEF is a regular hexagon where centre O is the origin.
If the position vectors of A and B are î - ĵ + 2k̂ and 2î + ĵ - k̂ respectively, then B̅C̅ is equal to
(a) î + ĵ - 2k̂
(b) -î + ĵ - 2k̂
(c) 3î + 3ĵ - 4k̂
(d) None of these
Answer: b

Question. Three points (2, –1, 3), (3, –5, 1) and (– 1, 11, 9) are
(a) Non-collinear
(b) Non-coplanar
(c) Collinear
(d) None of these
Answer: c

Question. If p, q, r be three non-zero vectors, then equation p .q = p . r implies:
(a) q = r
(b) p is orthogonal to both q and r.
(c) p is orthogonal to q – r.
(d) either q = r or p is perpendicular to q – r.
Answer: d

Question. If a̅ , b̅, c̅ are vectors such that [a̅ b̅ c̅] = 4, then [a̅ x b̅ b̅ x c̅ c̅ x a̅] =
(a) 16
(b) 64
(c) 4
(d) 8
Answer: a

Question. | (a × b).c| = |a| |b||c| , if
(a) a.b = b. c = 0
(b) b.c = c. a = 0
(c) c.a = a.b = 0
(d) a.b = b.c = c.a = 0 
Answer: d

Question. If C is the middle point of AB and P is any point outside AB, then
(a) P̅A̅ + P̅B̅ + = P̅C̅
(b) P̅A̅ + P̅B̅ + = 2P̅C̅
(c) P̅A̅ + P̅B̅ + = P̅C̅ = O̅
(d) P̅A̅ + P̅B̅ + = 2P̅C̅ = O̅
Answer: b

Question. If unit vector c̅ makes an angle π/3 with î + ĵ , then minimum and maximum values of (î x ĵ) .c̅ respectively are
(a) 0, √3/2
(b) -√3/2 , √3/2
(c) -1 , √3/2
(d) None of these
Answer: b

Question. If ABCDE is a pentagon, then resultant of AB, AE, BC, DC, ED and AC is
(a) 2AC
(b) 3AC
(c) AB
(d) None of these
Answer: b

Question. The non-zero vectors a, b and c are related by a = 8b and c = – 7b, then the angle between a and c is
(a) π
(b) 0
(c) π/4
(d) π/2
Answer: a

Question. For any two vectors a and b, (a × b)² equals
(a) a²b² – (a.b)²
(b) a² + b²
(c) a² – b²
(d) None of these
Answer: a

Question. The dot product of a vector with the vectors î + ĵ - 3k̂, î + 3ĵ - 2k̂and 2î + ĵ -4k̂ are 0, 5 and 8 respectively. Find the vector.
(a) î + 2ĵ + k̂
(b) -î + 3ĵ + 2k̂
(c) î + 2ĵ + 3k̂
(d) î - 3ĵ - 3k̂
Answer: a