# A force is 60 ° inclined to the horizontal. If its rectangular component in the horizontal direction is 50 N, then the magnitude of the force in the vertical direction is 1. 25 N 2. 75 N 3. 87 N 4. 100 N

Subtopic:  Resolution of Vectors |
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The component of vector $\stackrel{\to }{A}=3\stackrel{^}{i}+\stackrel{^}{j}+\stackrel{^}{k}$ along the direction of $\stackrel{^}{i}-\stackrel{^}{j}$ is:

1. $\sqrt{2}$

2. 2

3. $\sqrt{3}$

4. 3

Subtopic:  Scalar Product |
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If $\left|\stackrel{\to }{{\mathrm{v}}_{1}}+\stackrel{\to }{{\mathrm{v}}_{2}}\right|=\left|\stackrel{\to }{{\mathrm{v}}_{1}}-\stackrel{\to }{{\mathrm{v}}_{2}}\right|$ and $\stackrel{\to }{{\mathrm{v}}_{1}}$ and $\stackrel{\to }{{\mathrm{v}}_{2}}$ are non-zero vectors, then :

1. $\stackrel{\to }{{\mathrm{v}}_{1}}$ is parallel to $\stackrel{\to }{{\mathrm{v}}_{2}}$

2. $\stackrel{\to }{{\mathrm{v}}_{1}}$$\stackrel{\to }{{\mathrm{v}}_{2}}$

3. $\stackrel{\to }{{\mathrm{v}}_{1}}$ and $\stackrel{\to }{{\mathrm{v}}_{2}}$ are mutually perpendicular

4. $\left|\stackrel{\to }{{\mathrm{v}}_{1}}\right|=\left|\stackrel{\to }{{\mathrm{v}}_{2}}\right|$

Subtopic:  Resultant of Vectors |
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If $\stackrel{\to }{\mathrm{A}}=\stackrel{\to }{B}+\stackrel{\to }{C}$, and the magnitudes of $\stackrel{\to }{\mathrm{A}},\stackrel{\to }{B},\stackrel{\to }{C}$ are 5, 4 and 3 units, respectively. Then the angle between  is:

1. ${\mathrm{cos}}^{-1}\left(\frac{3}{5}\right)$

2. ${\mathrm{cos}}^{-1}\left(\frac{4}{5}\right)$

3. ${\mathrm{sin}}^{-1}\left(\frac{3}{4}\right)$

4. $\frac{\mathrm{\pi }}{2}$

Subtopic:  Resultant of Vectors |
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If vector  and  are functions of time, then the value of t at which they are orthogonal to each other will be:

1.

2.

3.

4.

Subtopic:  Scalar Product |
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Component of $3\stackrel{^}{\mathrm{i}}+4\stackrel{^}{\mathrm{j}}$ perpendicular to $\stackrel{^}{\mathrm{i}}+\stackrel{^}{\mathrm{j}}$ and in the same plane as that of $3\stackrel{^}{\mathrm{i}}+4\stackrel{^}{\mathrm{j}}$ is:

1.  $\frac{1}{2}\left(\stackrel{^}{\mathrm{j}}-\stackrel{^}{\mathrm{i}}\right)$

2.  $\frac{3}{2}\left(\stackrel{^}{\mathrm{j}}-\stackrel{^}{\mathrm{i}}\right)$

3.  $\frac{5}{2}\left(\stackrel{^}{\mathrm{j}}-\stackrel{^}{\mathrm{i}}\right)$

4.  $\frac{7}{2}\left(\stackrel{^}{\mathrm{j}}-\stackrel{^}{\mathrm{i}}\right)$

Subtopic:  Scalar Product |
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At what angle must the two forces (x + y) and (x y) act so that the resultant comes out to be $\left(\sqrt{{\mathrm{x}}^{2}+{\mathrm{y}}^{2}}\right)$ ?

1. ${\mathrm{cos}}^{-1}\left(-\frac{{\mathrm{x}}^{2}+{\mathrm{y}}^{2}}{2\left({\mathrm{x}}^{2}-{\mathrm{y}}^{2}\right)}\right)$

2. ${\mathrm{cos}}^{-1}\left(-\frac{2\left({\mathrm{x}}^{2}-{\mathrm{y}}^{2}\right)}{{\mathrm{x}}^{2}+{\mathrm{y}}^{2}}\right)$

3. ${\mathrm{cos}}^{-1}\left(-\frac{{\mathrm{x}}^{2}+{\mathrm{y}}^{2}}{{\mathrm{x}}^{2}-{\mathrm{y}}^{2}}\right)$

4. ${\mathrm{cos}}^{-1}\left(-\frac{{\mathrm{x}}^{2}-{\mathrm{y}}^{2}}{{\mathrm{x}}^{2}+{\mathrm{y}}^{2}}\right)$

Subtopic:  Resultant of Vectors |
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For the given figure, which of the following is true?

1. $\stackrel{\to }{\mathrm{B}}$ = $\stackrel{\to }{\mathrm{A}}$ + $\stackrel{\to }{\mathrm{C}}$

2. $\stackrel{\to }{\mathrm{A}}$ = $\stackrel{\to }{\mathrm{B}}$ + $\stackrel{\to }{\mathrm{C}}$

3. $\stackrel{\to }{\mathrm{C}}$$\stackrel{\to }{\mathrm{A}}$ + $\stackrel{\to }{\mathrm{B}}$

4. All of these

Subtopic:  Resultant of Vectors |
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The value of the unit vector, which is perpendicular to both A = $$\hat{i} + 2\hat{j} + 3 \hat{k}$$ and B = $$\hat{i} - 2\hat{j} - 3 \hat{k}$$ $\mathrm{is equal to}$:

1.

2.

3.

4.

Subtopic:  Vector Product |
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The instantaneous velocity (defined as $v=\frac{ds}{dt}$) at time $t=\frac{\mathrm{\pi }}{2}$ of a particle, whose position equation is given as  s(t)=12 tan$\left(\frac{t}{2}+\mathrm{\pi }\right)$m, is

1. 12 m/s
2. 12$\sqrt{2}$ m/s
3. 6 m/s
4. $$6\sqrt2$$ m/s

Subtopic:  Differentiation |
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