The component of vector [latex]hat{A}= 2hat{i}+3hat{j}[/latex] along the vector [latex]hat{i}+hat{j}[/latex] is 1) 5/√2 2) 10√2 3) 5√2 4) 5 Answer: 1) 5/√2 Solution:... View Article
[latex]vec{A}[/latex] is a vector with magnitude A, then the unit vector [latex]hat{A}[/latex] in the direction of [latex]vec{A}[/latex] is 1) 2) 3) 4) Answer: 4) Solution:... View Article
Position of a particle in a rectangular coordinate system is (3, 2, 5). Then, its position vector will be 1) 2) 3) 4) None of the above Answer: 2) If the point has coordinate (x,y,z) then the position vector is ... View Article
The area of the triangle formed by [latex]2hat{i}+hat{j}-hat{k}[/latex] and [latex]hat{i}+hat{j}+hat{k}[/latex] is 1) 3 sq units 2) 2√3 sq units 3) 2√14 sq units 4) √14/2 sq units Answer: 4) √14/2 sq units Solution: Area of the triangle = ... View Article
Which of the following is the unit vector perpendicular to [latex]vec{A}[/latex] and [latex]vec{B}[/latex]? 1) 2) 3) 4) Answer: 3) Solution: Vector perpendicular to A and B, Unit vector... View Article
Two forces F1 = 1 N and F2 = 2 N act along the lines x =0 and y =0 respectively. Then, the resultant of forces would be 1) 2) 3) 4) Answer: 4) Solution: x = 0 means y-axis ⇒ y = 0 means... View Article
Which of the following is independent of the choice of the coordinate system? 1) 2) (Px+Qx+Rx)i 3) 4) None of these Answer: 1) Solution: is independent of the coordinate system... View Article
A particle acted upon by constant forces [latex]4hat{i}+hat{j}-3hat{k}[/latex] and [latex]3hat{i}+hat{j}-hat{k}[/latex] is displaced from the point [latex]hat{i}+2hat{j}-3hat{k}[/latex] to point [latex]5hat{i}+4hat{j}-hat{k}[/latex]. The total work done by the forces in SI unit is 1) 20 2) 24 3) 50 4) 30 5) 35 Answer: 2) 24 Solution: Displacement , ... View Article
A particle has an initial velocity [latex]3hat{i}+4hat{j}[/latex] and an acceleration of [latex]0.4hat{i}+0.3hat{j}[/latex]. Its speed after 10s is 1) 10 units 2) 7 units 3) units 4) 8.5 units Answer: 3) units Solution: Initial velocity Acceleration ... View Article
the angle between the vectors a and b 1) cos-1(-1/3) 2)Â cos-1(1/4) 3)Â cos-1(-1/2) 4)Â cos-1(-1/6) Answer:Â 1) cos-1(-1/3) Solution: Angle between vectors , , , , = cos... View Article
The (x, y, z) coordinates of two points A and B are given respectively, as (0, 3, –1) and (–2, 6, 4). The displacement vector from A to B may be given by 1) 2) 3) 4) Answer: 3) Solution: Displacement vector... View Article
The magnitude of a vector on the addition of two vectors [latex]6\hat{i}+7\hat{j}[/latex] and [latex]3\hat{i}+4\hat{j}[/latex] 1) 2) 3) 4) Answer: 4) Solution: Sum of two vectors = A+B = = Magnitude of two... View Article
The coordinates of a particle moving in XY-plane at any instant of time t are x = 4t2, y = 3t2. The speed of the particle at that instant is 1) 10 t 2) 5 t 3) 3 t 4) 2 t 5) √13 t Answer: 1) 10 t Solution: Position vector Differentiating w.r.t to t... View Article
If A = B + C and the values of A, B and C are 13, 12 and 5 respectively, then the angle between A and C will be 1) cos-1(5/13) 2) cos-1(13/12) 3) π/2 4) sin-1 (5/12) Answer: 1) cos-1(5/13) Solution: The resultant A = √B2 +C2+2BCcosθ (13)2 =... View Article
If the angle between two vectors A and B is 120°, then its resultant C will be 1) C = |A–B| 2) C < |A–B| 3) C > |A–B| 4) C = |A+B| Answer: 2) C < |A–B| Solution: C is... View Article
A moves with 65 km/h while B is coming back of A with 80 km/h. The relative velocity of B with respect to A is 1) 80 km/h 2) 60 km/h 3) 15 km/h 4) 145 km/h Answer: 4) 145 km/h Solution: Relative velocity of B w.r.t A VBA = VB - VA = 80 - (-65)... View Article
If a body is in equilibrium under a set of non-collinear forces, then the minimum number of forces has to be 1) Four 2) Three 3) Two 4) Five Answer: 2) Three Solution: Since the forces are in equilibrium under a set of non-collinear forces at... View Article
Three vectors [latex]vec{a}[/latex],[latex]vec{b}[/latex] and [latex]vec{c}[/latex] satisfy the relation [latex]vec{a}.vec{b}=0[/latex] and [latex]vec{a}.vec{c}=0[/latex]. The vector [latex]vec{a}[/latex] is parallel to 1)Â 2)Â 3)Â 4)Â Answer:Â 4)Â Solution: will be perpendicular to each other will be perpendicular to each other... View Article
If [latex]\left | \vec{A}\times \vec{B} \right |=\left | \vec{A}.\vec{B} \right |[/latex], then angle between [latex]\vec{A}[/latex] and [latex]\vec{B}[/latex] will be 1) 300 2) 450 3) 600 4) 900 Answer: 2) 450 Solution: θ=450... View Article
