Select Chapter Topics: If vectors $\stackrel{\to }{\mathrm{A}}=\mathrm{cos\omega t}\stackrel{^}{\mathrm{i}}+\mathrm{sin\omega t}\stackrel{^}{\mathrm{j}}$ and $\stackrel{\to }{\mathrm{B}}=\mathrm{cos}$ $\frac{\mathrm{\omega t}}{2}\stackrel{^}{\mathrm{i}}+\mathrm{sin}$ $\frac{\mathrm{\omega t}}{2}\stackrel{^}{\mathrm{j}}$ 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 |
59%
From NCERT
NEET - 2015
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Hints
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Vectors $$\vec {\mathrm{A}}, \vec{\mathrm{B}}$$ and $$\vec{\mathrm{C}}$$ are such that $$\vec{\mathrm{A}} \cdot \vec{\mathrm{B}}=0 \text { and } \vec{\mathrm{A}} \cdot \vec{\mathrm{C}}=0$$. Then the vector parallel to $$\vec A$$ is:
1. $$\vec{A} \times \vec{B}$$
2. $$\vec{B}+\vec{C}$$
3. $$\vec{B} \times \vec{C}$$
4. $$\vec{B}~\text{and} ~\vec{C}$$  Subtopic:  Vector Product |
70%
From NCERT
NEET - 2013
Hints

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 |
74%
From NCERT
AIPMT - 2010
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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.  $0.5$ $\mathrm{N}$

2.  $1.5$ $\mathrm{N}$

3.  $\frac{\sqrt{3}}{4}$ $\mathrm{N}$

4.  $\sqrt{3}$ $\mathrm{N}$  Subtopic:  Resultant of Vectors |
52%
From NCERT
AIPMT - 2008
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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 |
79%
From NCERT
AIPMT - 2007
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The vectors $\stackrel{\to }{\mathrm{A}}$ $\mathrm{and}$ $\stackrel{\to }{\mathrm{B}}$ 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. $$90^\circ$$
2. $$60^\circ$$
3. $$75^\circ$$
4. $$45^\circ$$  Subtopic:  Resultant of Vectors |
79%
From NCERT
AIPMT - 2006
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NEET 2023 - Target Batch - Aryan Raj Singh
Hints
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Select Chapter Topics: 