JEE & NEETJEE Mathematics JEE Main Maths 100+ MCQ & Answer | Page-09 | JEE & NEET MCQ February 4, 2025 DSN MARATHI 81. The summation of two unit vectors is a third unit vector, then the modulus of the difference of the unit vector is A. √3 B. 1 – √3 C. 1 + √3 D. -√3 Answer Option : A 82. The vectors λi^+j^+2k^,i^+λj^−k^ and 2i^−j^+λk^ are coplanar if A. λ = -2 B. λ = 0 C. λ = 1 D. λ = -1 Answer Option : A 83. If |a| = 4 and -3 ≤ λ ≤ 2, then the range of |λa| is A. [0, 8] B. [-12, 8] C. [0, 12] D. [8, 12] Answer Option : C 84. The number of vectors of unit length perpendicular to the vectors a = 2i^+j^+2k^ and b = j^+k^ is A. one B. two C. three D. infinite Answer Option : B 85. Let a, b and c be vectors with magnitudes 3, 4 and 5 respectively and a + b + c = 0, then the values of a.b + b.c + c.a is A. 47 B. 25 C. 50 D. -25 Answer Option : D 86. a, b, c are three vectors, such that a + b + c = 0, |a|= 1, |b|= 2, |c|= 3, then a.b + b.c + c is equal to A. 0 B. -7 C. 7 D. 1 Answer Option : B 87. If the angle between i^+k^ and i^+j^+ak^ is π3, then the value of a is A. 0 or 2 B. -4 or 0 C. 0 or -3 D. 2 or -2 Answer Option : B 88. Find the magnitude of vector 3i^+2j^+12k^. A. √157 B. 4√11 C. √213 D. 9√3 Answer Option : A 89. Which of the following represents equal vectors? A. a, c B. b, d C. b, c D. m, d Answer Option : B 90. Which of the following represents collinear but not equal vectors? A. a, c B. b, d C. b, m D. Both (a) and (b) Answer Option : A
81. The summation of two unit vectors is a third unit vector, then the modulus of the difference of the unit vector is A. √3 B. 1 – √3 C. 1 + √3 D. -√3 Answer Option : A
82. The vectors λi^+j^+2k^,i^+λj^−k^ and 2i^−j^+λk^ are coplanar if A. λ = -2 B. λ = 0 C. λ = 1 D. λ = -1 Answer Option : A
83. If |a| = 4 and -3 ≤ λ ≤ 2, then the range of |λa| is A. [0, 8] B. [-12, 8] C. [0, 12] D. [8, 12] Answer Option : C
84. The number of vectors of unit length perpendicular to the vectors a = 2i^+j^+2k^ and b = j^+k^ is A. one B. two C. three D. infinite Answer Option : B
85. Let a, b and c be vectors with magnitudes 3, 4 and 5 respectively and a + b + c = 0, then the values of a.b + b.c + c.a is A. 47 B. 25 C. 50 D. -25 Answer Option : D
86. a, b, c are three vectors, such that a + b + c = 0, |a|= 1, |b|= 2, |c|= 3, then a.b + b.c + c is equal to A. 0 B. -7 C. 7 D. 1 Answer Option : B
87. If the angle between i^+k^ and i^+j^+ak^ is π3, then the value of a is A. 0 or 2 B. -4 or 0 C. 0 or -3 D. 2 or -2 Answer Option : B
89. Which of the following represents equal vectors? A. a, c B. b, d C. b, c D. m, d Answer Option : B
90. Which of the following represents collinear but not equal vectors? A. a, c B. b, d C. b, m D. Both (a) and (b) Answer Option : A
