If $$\vec F=2\hat i+\hat j-\hat k$$ and $$\vec r=3\hat i+2\hat j-2\hat k,$$ then the scalar and vector products of $$\vec F$$ and $$\vec r$$ have the magnitudes, respectively, as:
1.  $$5, ~\sqrt3$$
2.  $$4,~ \sqrt5$$
3.  $$10, ~\sqrt2$$
4.  $$10,~2$$
Subtopic:  Vector Product |
75%
From NCERT
NEET - 2022
To view explanation, please take trial in the course.
NEET 2023 - Target Batch - Aryan Raj Singh
Hints
To view explanation, please take trial in the course.
NEET 2023 - Target Batch - Aryan Raj Singh

A particle moves from a point $$\left(\right. - 2 \hat{i} + 5 \hat{j} \left.\right)$$ to $$\left(\right. 4 \hat{j} + 3 \hat{k} \left.\right)$$ when a force of $$\left(\right. 4 \hat{i} + 3 \hat{j} \left.\right)$$ $$\text{N}$$ 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 |
63%
From NCERT
NEET - 2016
To view explanation, please take trial in the course.
NEET 2023 - Target Batch - Aryan Raj Singh
Hints
To view explanation, please take trial in the course.
NEET 2023 - Target Batch - Aryan Raj Singh

If the magnitude of the sum of two vectors is equal to the magnitude of the difference between the two vectors, the angle between these vectors is?
1. $$90^\circ$$
2. $$45^\circ$$
3. $$180^\circ$$
4. $$0^\circ$$
Subtopic:  Resultant of Vectors |
82%
From NCERT
NEET - 2016
To view explanation, please take trial in the course.
NEET 2023 - Target Batch - Aryan Raj Singh
Hints
To view explanation, please take trial in the course.
NEET 2023 - Target Batch - Aryan Raj Singh

If vectors $$\overrightarrow{{A}}=\cos \omega t \hat{{i}}+\sin \omega t \hat{j}$$ and $$\overrightarrow{{B}}=\cos \left(\frac{\omega t}{2}\right)\hat{{i}}+\sin \left(\frac{\omega t}{2}\right) \hat{j}$$ are functions of time. Then, at what value of $$t$$ are they orthogonal to one another?
1. $$t = \frac{\pi}{4\omega}$$
2. $$t = \frac{\pi}{2\omega}$$
3. $$t = \frac{\pi}{\omega}$$
4. $$t = 0$$

Subtopic:  Scalar Product |
59%
From NCERT
NEET - 2015
To view explanation, please take trial in the course.
NEET 2023 - Target Batch - Aryan Raj Singh
Hints
To view explanation, please take trial in the course.
NEET 2023 - Target Batch - Aryan Raj Singh

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
To view explanation, please take trial in the course.
NEET 2023 - Target Batch - Aryan Raj Singh
Hints
To view explanation, please take trial in the course.
NEET 2023 - Target Batch - Aryan Raj Singh

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
To view explanation, please take trial in the course.
NEET 2023 - Target Batch - Aryan Raj Singh
Hints
To view explanation, please take trial in the course.
NEET 2023 - Target Batch - Aryan Raj Singh

$\stackrel{\to }{\mathrm{A}}$ 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 |
80%
From NCERT
AIPMT - 2007
To view explanation, please take trial in the course.
NEET 2023 - Target Batch - Aryan Raj Singh
Hints
To view explanation, please take trial in the course.
NEET 2023 - Target Batch - Aryan Raj Singh

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 |
80%
From NCERT
AIPMT - 2006
To view explanation, please take trial in the course.
NEET 2023 - Target Batch - Aryan Raj Singh
Hints
To view explanation, please take trial in the course.
NEET 2023 - Target Batch - Aryan Raj Singh

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 |
75%
From NCERT
AIPMT - 2005
To view explanation, please take trial in the course.
NEET 2023 - Target Batch - Aryan Raj Singh
Hints
To view explanation, please take trial in the course.
NEET 2023 - Target Batch - Aryan Raj Singh

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 |
59%
From NCERT
AIPMT - 2005
To view explanation, please take trial in the course.
NEET 2023 - Target Batch - Aryan Raj Singh
Hints