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Position of a particle in a rectangular coordinate system is (3, 2, 5). Then, its position vector will be

1) \(\begin{array}{l}3\hat{i}+5\hat{j}+2\hat{k}\end{array} \) 2) \(\begin{array}{l}3\hat{i}+2\hat{j}+5\hat{k}\end{array} \) 3) \(\begin{array}{l}5\hat{i}+3\hat{j}+2\hat{k}\end{array} \) 4) None of the above Answer: 2) \(\begin{array}{l}3\hat{i}+2\hat{j}+5\hat{k}\end{array} \) If the point has coordinate (x,y,z) then... 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: \(\begin{array}{l}\vec{A}=2\hat{i}+\hat{j}-\hat{k}\end{array}... View Article

Which of the following is the unit vector perpendicular to [latex]vec{A}[/latex] and [latex]vec{B}[/latex]?

1) \(\begin{array}{l}\frac{\hat{A}\times \hat{B}}{ABsin\theta }\end{array} \) 2) \(\begin{array}{l}\frac{\hat{A}\times \hat{B}}{ABcos\theta }\end{array} \) 3) \(\begin{array}{l}\frac{\vec{A}\times \vec{B}}{ABsin\theta }\end{array} \) 4) \(\begin{array}{l}\frac{\vec{A}\times \vec{B}}{ABcos\theta }\end{array} \) Answer: 3) \(\begin{array}{l}\frac{\vec{A}\times \vec{B}}{ABsin\theta }\end{array} \)... 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) \(\begin{array}{l}\hat{i}+2\hat{j}\end{array} \) 2) \(\begin{array}{l}\hat{i}+\hat{j}\end{array} \) 3) \(\begin{array}{l}3\hat{i}+2\hat{j}\end{array} \) 4) \(\begin{array}{l}2\hat{i}+\hat{j}\end{array} \) Answer: 4) \(\begin{array}{l}2\hat{i}+\hat{j}\end{array} \) Solution: x = 0 means y-axis ⇒ \(\begin{array}{l}\vec{F_{1}}=\hat{j}\end{array} \) y = 0... View Article

Which of the following is independent of the choice of the coordinate system?

1) \(\begin{array}{l}\vec{P}+\vec{Q}+\vec{R}\end{array} \) 2) (Px+Qx+Rx)i 3) \(\begin{array}{l}P_{x}\hat{i}+Q_{x}\hat{j}+R_{z}\hat{k}\end{array} \) 4) None of these Answer: 1) \(\begin{array}{l}\vec{P}+\vec{Q}+\vec{R}\end{array} \) Solution: \(\begin{array}{l}1)\vec{P}+\vec{Q}+\vec{R}\end{array} \) is independent of... 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: \(\begin{array}{l}F_{1}=4\hat{i}+\hat{j}-3\hat{k}\end{array} \) \(\begin{array}{l}F_{2}=3\hat{i}+\hat{j}-\hat{k}\end{array} \) \(\begin{array}{l}F_{1}+F_{2}= (4\hat{i}+\hat{j}-3\hat{k})... 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) \(\begin{array}{l}7\sqrt{2}\end{array} \) units 4) 8.5 units Answer: 3) \(\begin{array}{l}7\sqrt{2}\end{array} \) units Solution: Initial velocity \(\begin{array}{l}u = 3\hat{i}+4\hat{j}\end{array}... View Article

the angle between the vectors a and b

1) cos-1(-1/3) 2) cos-1(1/4) 3) cos-1(-1/2) 4) cos-1(-1/6) Answer: 1) cos-1(-1/3) Solution: Angle between vectors \(\begin{array}{l}a = 3\hat{i}-4\hat{j}\end{array} \) and \(\begin{array}{l}b = 2\hat{i}+3\hat{k}\end{array} \), \(\begin{array}{l}a... 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) \(\begin{array}{l}-2\hat{i}+6\hat{j}+4\hat{k}\end{array} \) 2) \(\begin{array}{l}-2\hat{i}+3\hat{j}+3\hat{k}\end{array} \) 3) \(\begin{array}{l}-2\hat{i}+3\hat{j}+5\hat{k}\end{array} \) 4) \(\begin{array}{l}2\hat{i}+3\hat{j}-5\hat{k}\end{array} \) Answer: 3) \(\begin{array}{l}-2\hat{i}+3\hat{j}+5\hat{k}\end{array} \) Solution: Displacement vector \(\begin{array}{l}r_{i}= 3\hat{j}-\hat{k}\end{array} \) \(\begin{array}{l}r_{i}=-2\hat{i}+6\hat{j}+4\hat{k}\end{array} \) \(\begin{array}{l}r_{f}-r_{i}=\Delta r=(-2\hat{i}+6\hat{j}+4\hat{k})-(3\hat{j}-\hat{k})\end{array}... 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) \(\begin{array}{l}\sqrt{132}\end{array} \) 2) \(\begin{array}{l}\sqrt{136}\end{array} \) 3) \(\begin{array}{l}\sqrt{160}\end{array} \) 4) \(\begin{array}{l}\sqrt{202}\end{array} \) Answer: 4) \(\begin{array}{l}\sqrt{202}\end{array} \) Solution: \(\begin{array}{l}A= 6\hat{i}+7\hat{j}\end{array} \) and \(\begin{array}{l}B= 3\hat{i}+4\hat{j}\end{array} \) Sum 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 \(\begin{array}{l}r... 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 = (12)2+(5)2+ 2(12)(5)... 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|... 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... 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... 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) \(\begin{array}{l}\vec{b}\end{array} \) 2) \(\begin{array}{l}\vec{c}\end{array} \) 3) \(\begin{array}{l}\vec{b}.\vec{c}\end{array} \) 4) \(\begin{array}{l}\vec{b}\times \vec{c}\end{array} \) Answer: 4) \(\begin{array}{l}\vec{b}\times \vec{c}\end{array} \) Solution: \(\begin{array}{l}\vec{a}. \vec{b}=0\end{array} \) i.e., \(\begin{array}{l}\vec{a}\end{array} \) and \(\begin{array}{l}\vec{b}\end{array} \)... View Article

In a clockwise system

1) \(\begin{array}{l}\hat{j}\times \hat{k}=\hat{i}\end{array} \) 2) \(\begin{array}{l}\hat{i}.\hat{i}= 0\end{array} \) 3) \(\begin{array}{l}\hat{j}\times \hat{j}= 1\end{array} \) 4) \(\begin{array}{l}\hat{k}.\hat{j}= 1\end{array} \) Answer: 1) \(\begin{array}{l}\hat{j}\times \hat{k}=\hat{i}\end{array} \) Solution: In a clockwise... 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: \(\begin{array}{l}\left | \vec{A}\times \vec{B} \right |=\vec{A}.\vec{B}\Rightarrow ABsin\theta =ABcos\theta \Rightarrow... View Article

The resultant of the two vectors having magnitude 2 and 3 is 1. What is their cross product?

1) 6 2) 3 3) 1 4) 0 Answer: 4) 0 Solution: \(\begin{array}{l}\sqrt{2^{2}+3^{2}+2\times 2\times 3\times cos\theta }=1\end{array} \) 1-4-9 =12cosθ cosθ... View Article

The area of the parallelogram represented by the vectors [latex]vec{A}=(2hat{i}+3hat{j})[/latex] and [latex]vec{B}=(hat{i}+4hat{j})[/latex]

1) 14 units 2) 7.5 units 3) 10 units 4) 5 units Answer: 4) 5 units Solution: \(\begin{array}{l}\left | \vec{A}\times \vec{B}... View Article

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