Title 1-introduction-to-vector--forces-.pdf ✅

Introduction to Vector & Forces 1. Three non-zero vectors A⃗, B⃗⃗ and C⃗ add up to zero. Find which is false? (A) (A⃗ × B⃗⃗) × C⃗ is not zero unless B⃗⃗, C⃗ are parallel (B) (A⃗ × B⃗⃗) ⋅ C⃗ is not zero unless B⃗⃗, C⃗ are parallel (C) If A⃗, B⃗⃗, C⃗ define a plane, (A⃗ × B⃗⃗) × C⃗ is in that plane (D) (A⃗ × B⃗⃗) ⋅ C⃗ = |A||B||C| ⇒ C 2 = A 2 + B 2 2. When in going east at 10kmph, a train moving with constant velocity appears to be moving exactly 'northeast'. When my velocity is increased to 30kmph east it appears to be moving north. With what speed should i move north so that train appears to be moving exactly south-east? (A) 30 (B) 20 (C) 50 (D) 10 3. A wedge of mass M rests on a smooth horizontal surface. It is placed against a smooth vertical wall as shown. A force F is applied to the inclined surface (i) horizontally (ii) vertically (iii) ⊥ to the inclined surface. (i) (ii) (iii) Let R be normal force between wall and block and N be normal force between ground and the block. Then for the three cases : (A) (i) R = F, N = Mg (B) (i) R = F, N = Mg (iii) (F + Mg)sin θ = R (ii) R = 0, N = Mg + F (iii) R = Fsin θ, F + Mgcos θ = N (iii) R = Fsin θ, N = Mg + Fcos θ (C) N = Mg for each case and R = F, 0 and mgsin θ (D) None of these 4. It is found that |A⃗ + B⃗⃗| = |A⃗|. This necessarily implies: (A) B⃗⃗ = 0⃗⃗ (B) A⃗, B⃗⃗ are anti-parallel
(C) A⃗, B⃗⃗ are perpendicular (D) A⃗ ⋅ B⃗⃗ ≤ 0 5. Let there be two vectors a⃗ and b⃗⃗ such that a⃗ + b⃗⃗ is in same direction as a⃗ − b⃗⃗. Select the correct alternative. (A) a⃗ × b⃗⃗ = 0⃗⃗ (B) |a⃗| > |b⃗⃗| (C) Both (A) & (B) must be simultaneously true (D) a⃗ ⋅ b⃗⃗ = 0 6. If a⃗ denotes a unit vector along an incident light, b⃗⃗ a unit vector along refracted ray into a medium having refractive index x (relative to first medium) and c⃗ is a unit vector normal to boundary of two media and directed towards first medium , then law of refraction is (A) a⃗ ⋅ c⃗ = x(b⃗⃗ ⋅ c⃗) (B) a⃗ × c⃗ = x(b⃗⃗ × c⃗) (C) c⃗ × a⃗ = x(b⃗⃗ × c⃗) (D) x(a⃗ × c⃗) = b⃗⃗ × c⃗ 7. If A ̅ and B ̅ are the components of C⃗, then : (A) A = √3 2 C (B) B = C √2 (C) A = 2C √3+1 (D) B = √2(√3 − 1)C 8. For two vectors A⃗ and B⃗⃗, |A⃗ + B⃗⃗| = |A⃗ − B⃗⃗| is always true when : (A) |A⃗| = |B⃗⃗| ≠ 0 (B) A⃗ ⊥ B⃗⃗ (C) |A⃗| = |B⃗⃗| ≠ 0 and A⃗ and B⃗⃗ are parallel or anti parallel (D) Either |A⃗| or |B⃗⃗| is zero 9. Regarding non-zero vectors, which of the following is a correct statement : (A) Two equal vectors can never give an addition resultant equal to null - vector. (B) Three non-coplanar vectors can not give zero vector addition resultant (C) If a⃗ ⋅ (b⃗⃗ × c⃗) = 0 and |a⃗| ≠ |b⃗⃗| ≠ |c⃗| then a⃗ + b⃗⃗ + c⃗ can never be aull vector (D) If a⃗ × b⃗⃗ = 0⃗⃗ and |a⃗| = |b⃗⃗|, then a⃗ + b⃗⃗ can be zero vectors. 10. The friction coefficient between the board and the floor shown in figure is μ. The maximum force that the man can exert on the rope so that the board does not slip on the floor is : ( m is mass of man and M is mass of plank) (A) μ(M+m)g (1+μ) (B) μ(M−m)g (1+μ) (C) μ M m g (D) None of these 11. A block of mass 4 kg is acted upon by a 50 N force a shown. The friction coefficient between block and wall is μ. (A) For μ = 0.5 block will be at rest (B) For μ = 0.2 block will move down (C) For μ = 0.8 block will move up (D) Block can never move up for any value of μ 12. Given a parallelogram ABCD. If |AB⃗⃗⃗⃗⃗⃗| = a, |AD⃗⃗⃗⃗⃗⃗| = b&|AC⃗⃗⃗⃗⃗⃗| = c then DB⃗⃗ ⋅ AB⃗⃗ has the value (A) 2a 2+b 2−c 2 2