The position of a particle in a rectangular co-ordinate system is (3, 2, 5). Then its position vector will be:

1. $5\stackrel{^}{\mathrm{i}}+6\stackrel{^}{\mathrm{j}}+2\stackrel{^}{\mathrm{k}}$

2. $3\stackrel{^}{\mathrm{i}}+2\stackrel{^}{\mathrm{j}}+5\stackrel{^}{\mathrm{k}}$

3. $5\stackrel{^}{\mathrm{i}}+3\stackrel{^}{\mathrm{j}}+2\stackrel{^}{\mathrm{k}}$

4. None of these

Subtopic:  Scalars & Vectors |
92%
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A scalar quantity is one that:

 1 is conserved in a process. 2 will never accept negative values. 3 must be dimensionless. 4 has the same value for observers with different orientations of axes.

Subtopic:  Scalars & Vectors |
61%
From NCERT
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If $$\vec{a}$$ is a vector and $$x$$ is a non-zero scalar, then which of the following is correct?
1. $$x\vec{a}$$ is a vector in the direction of $$\vec{a}$$
2. $$x\vec{a}$$ is a vector collinear to $$\vec{a}$$
3. $$x\vec{a}$$ and $$\vec{a}$$ have independent directions
4. $$x\vec{a}$$ is a vector perpendicular to $$\vec{a}$$

Subtopic:  Scalars & Vectors |
From NCERT
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If $\stackrel{\to }{\mathrm{A}}=2\stackrel{^}{\mathrm{i}}+4\stackrel{^}{\mathrm{j}}-5\stackrel{^}{\mathrm{k}}$, then the direction cosines of the vector are:

(direction cosines (or directional cosines) of a vector are the cosines of the angles between the vector and the three +ve coordinate axes.)

1.

2.

3.

4.

Subtopic:  Resolution of Vectors |
88%
From NCERT
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A force $$\mathrm{F}$$ applied at a $$30^\circ$$ angle to the $$\mathrm{x }$$-axis has the following X and Y components:

1.

2.

3.

4.

Subtopic:  Resolution of Vectors |
79%
From NCERT
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A child pulls a box with a force of  at an angle of $60°$above the horizontal. Then the horizontal and vertical components of the force will be:

1. 100 N, 175 N

2.  86.6 N, 100 N

3.  100 N, 86.6 N

4. 100 N, 0 N

Subtopic:  Resolution of Vectors |
69%
From NCERT
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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 |
59%
From NCERT
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Figure shows the orientation of two vectors u and v in the XY plane.

Which of the following is correct?

1. a and p are positive while b and q are negative

2. a, p, and b are positive while q is negative

3. a, q, and b are positive while p is negative

4. a, b, p, and q are all positive

Subtopic:  Resolution of Vectors |
56%
From NCERT
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A certain vector in the xy-plane has an x-component of $$4$$ m and a y-component of $$10$$ m. It is then rotated in the xy-plane so that its x-component is doubled. Then, its new y-component will be: (approximately)
1. $$20$$ m
2. $$7.2$$ m
3. $$5.0$$ m
4. $$4.5$$ m
Subtopic:  Resolution of Vectors |
52%
From NCERT
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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 |
77%
From NCERT
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