# A particle moves from a point $\left(-2\stackrel{^}{\mathrm{i}}+5\stackrel{^}{\mathrm{j}}\right)$ to $\left(4\stackrel{^}{\mathrm{j}}+3\stackrel{^}{\mathrm{k}}\right)$ when a force of  is applied. How much work has been done by the force? 1.  8 J 2.  11 J 3.  5 J 4.  2 J

Subtopic:  Scalar Product |
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If the magnitude of the sum of two vectors is equal to the magnitude of difference of the two vectors, the angle between these vectors is

1. 90o

2. 45o

3. 180o

4. 0o

Subtopic:  Resultant of Vectors |
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If vectors $\stackrel{\to }{\mathrm{A}}=\mathrm{cos\omega t}\stackrel{^}{\mathrm{i}}+\mathrm{sin\omega t}\stackrel{^}{\mathrm{j}}$ and  are functions of time. Then, at what value of t are they orthogonal to one another?

1. $\mathrm{t}=\frac{\mathrm{\pi }}{4\mathrm{\omega }}$

2. $\mathrm{t}=\frac{\mathrm{\pi }}{2\mathrm{\omega }}$

3. $\mathrm{t}=\frac{\mathrm{\pi }}{\mathrm{\omega }}$

4. $\mathrm{t}=0$

Subtopic:  Scalar Product |
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Six vectors $\stackrel{\to }{\mathrm{a}}$ through $\stackrel{\to }{\mathrm{f}}$ have the magnitudes and directions indicated in the figure. Which of the following statements is true? 1. $\stackrel{\to }{\mathrm{b}}+\stackrel{\to }{\mathrm{c}}=\stackrel{\to }{\mathrm{f}}$

2. $\stackrel{\to }{\mathrm{d}}+\stackrel{\to }{\mathrm{c}}=\stackrel{\to }{\mathrm{f}}$

3. $\stackrel{\to }{\mathrm{d}}+\stackrel{\to }{\mathrm{e}}=\stackrel{\to }{\mathrm{f}}$

4. $\stackrel{\to }{\mathrm{b}}+\stackrel{\to }{\mathrm{e}}=\stackrel{\to }{\mathrm{f}}$

Subtopic:  Resultant of Vectors |
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Three forces acting on a body are shown in the figure. To have the resultant force only along the y-direction, the magnitude of the minimum additional force needed is 1.

2.

3.

4.

Subtopic:  Resultant of Vectors |
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$\stackrel{\to }{\mathrm{A}}$ and $\stackrel{\to }{\mathrm{B}}$ are two vectors and θ is the angle between them. If $\left|\stackrel{\to }{\mathrm{A}}×\stackrel{\to }{\mathrm{B}}\right|=\sqrt{3}\left(\stackrel{\to }{A}.\stackrel{\to }{B}\right)$, then the value of θ will be:

1. 60o

2. 45o

3. 30o

4. 90o

Subtopic:  Scalar Product | Vector Product |
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The vectors  are such that: $\left|\stackrel{\to }{\mathrm{A}}+\stackrel{\to }{\mathrm{B}}\right|=\left|\stackrel{\to }{\mathrm{A}}-\stackrel{\to }{\mathrm{B}}\right|$.
The angle between the two vectors is:

1. 90o

2. 60o

3. 75o

4. 45o

Subtopic:  Resultant of Vectors |
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If a vector ($2\stackrel{^}{\mathrm{i}}+3\stackrel{^}{j}+8\stackrel{^}{k}$) is perpendicular to the vector ($4\stackrel{^}{\mathrm{i}}-4\stackrel{^}{j}+\mathrm{\alpha }\stackrel{^}{k}$), then the value of $\mathrm{\alpha is}$

1. -1

2. $-\frac{1}{2}$

3. $\frac{1}{2}$

4. 1

Subtopic:  Scalar Product |
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If the angle between the vector is θ, the value of the product $\left(\stackrel{\to }{\mathrm{B}}×\stackrel{\to }{\mathrm{A}}\right)\cdot \stackrel{\to }{\mathrm{A}}$ is equal to

1. zero

2. BA2sinθcosθ

3. BA2cosθ

4. BA2sinθ

Subtopic:  Scalar Product | Vector Product |
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1. ${\left({\mathrm{A}}^{2}+{\mathrm{B}}^{2}+\frac{\mathrm{AB}}{\sqrt{3}}\right)}^{1/2}$

2. A+B

3. ${\left({\mathrm{A}}^{2}+{\mathrm{B}}^{2}+\sqrt{3}\mathrm{AB}\right)}^{1/2}$

4. ${\left({\mathrm{A}}^{2}+{\mathrm{B}}^{2}+\mathrm{AB}\right)}^{1/2}$

Subtopic:  Scalar Product | Vector Product |
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