Vectors worksheet for Class 11 Physics

Which of the following is a vector quantity?

1. a Work
2. b Displacement
3. c Power
4. d Time

Two forces of 6 N and 8 N act on a particle in mutually perpendicular directions. The magnitude of the resultant force will be:

1. a 14 N
2. b 12 N
3. c 10 N
4. d 7 N

If the magnitude of the resultant of two vectors equal in magnitude is also equal to their individual magnitude, then the angle between the two vectors will be:

1. a $2\pi/3$
2. b $2\pi/2$
3. c $\pi/3$
4. d $0$

If $\hat a$ is a unit vector in the direction of the vector $\vec A$, then:

1. a $\hat a = |\vec A|\,\vec A$
2. b $\hat a = |\vec A|/\vec A$
3. c $\hat a = \vec A/\vec A$
4. d $\hat a = \vec A/|\vec A|$

Find $p$ if $\vec a = p\,\hat\imath + 0.3\,\hat\jmath + 0.4\,\hat k$ is a unit vector.

1. a $0.5$
2. b $0.5\sqrt{3}$
3. c $0.5\sqrt{2}$
4. d $0.75$

If a unit vector is represented by $(0.5\,\hat\imath + 0.8\,\hat\jmath + c\,\hat k)$, then the value of $c$ is:

1. a $1$
2. b $\sqrt{0.11}$
3. c $\sqrt{0.01}$
4. d $\sqrt{0.39}$

Two vectors $\vec A$ and $\vec B$ are mutually perpendicular if:

1. a $\vec A \times \vec B = 0$
2. b $\vec A \cdot \vec B = 0$
3. c $\vec A + \vec B = 0$
4. d $\vec A \cdot \vec B = 1$

If a vector is $\vec F = 4\hat\imath - 3\hat\jmath$, then a vector perpendicular to this direction is:

1. a $4\hat\imath + 3\hat\jmath$
2. b $4\hat\imath - 3\hat\jmath$
3. c $7\hat k$
4. d $5\hat\imath$

If $\vec A = (\hat\imath + \hat\jmath)$ and $\vec B = \hat\imath$, find the angle between $\vec A$ and $\vec B$.

1. a $\pi/6$
2. b $\pi/4$
3. c $\pi/3$
4. d $\pi/2$

If $|\vec P \times \vec Q| = \vec P \cdot \vec Q$, then the angle between $\vec P$ and $\vec Q$ will be:

1. a $0$
2. b $\pi/4$
3. c $\pi/2$
4. d $\pi$

The magnitudes of two vectors are 4 and 3 respectively and the magnitude of their resultant is 1. The angle between these vectors is:

1. a $0$
2. b $\pi/4$
3. c $\pi/2$
4. d $\pi$

The vectors $\vec A = (3\hat\imath - 2\hat\jmath + \hat k)$ and $(2\hat\imath + 6\hat\jmath + p\hat k)$ will be mutually perpendicular if the value of $p$ is:

1. a $3$
2. b $6$
3. c $-3$
4. d $-6$

If $\vec P = 2\hat\imath + 5\hat k$ and $\vec Q = 3\hat\jmath + 4\hat k$, then their scalar product is:

1. a $20$
2. b $26$
3. c $23$
4. d $5\sqrt{29}$

The angle between $(\vec A + \vec B)$ and $(\vec A \times \vec B)$ is:

1. a Zero
2. b $\pi/4$
3. c $\pi/2$
4. d $\pi$

If $\hat\imath$, $\hat\jmath$ and $\hat k$ are unit vectors in the Cartesian coordinate system, then:

1. a $\hat\imath \cdot \hat\imath = 0$
2. b $\hat\jmath \times \hat k = 0$
3. c $\hat k \cdot \hat\jmath = 1$
4. d $\hat\imath \times \hat\jmath = \hat k$

What is the angle between $(\vec P \times \vec Q)$ and $(\vec Q \times \vec P)$?

1. a $0$
2. b $\pi/2$
3. c $2\pi/3$
4. d $\pi$

The magnitude of $\vec A \times \vec B$ cannot be:

1. a Equal to $AB$
2. b Less than $AB$
3. c Greater than $AB$
4. d None of these

The value of $(\hat\imath \times \hat\jmath) \cdot \hat\jmath$ will be:

1. a $1$
2. b $-1$
3. c Zero
4. d $-\hat k$

The value of $(\hat\imath \times \hat\jmath) \times \hat k$ will be:

1. a Zero
2. b $1$
3. c $-1$
4. d $\hat k$

If $|\vec V_1 + \vec V_2| = |\vec V_1 - \vec V_2|$ and $\vec V_1$, $\vec V_2$ are non-zero, then:

1. a $\vec V_1$ and $\vec V_2$ are parallel
2. b $\vec V_1$ and $\vec V_2$ are mutually perpendicular
3. c $|\vec V_1| = |\vec V_2|$
4. d $\vec V_1 = \vec V_2$

The incorrect relationship for vectors $\vec A$ and $\vec B$ is:

1. a $\vec A + \vec B = \vec B + \vec A$
2. b $\vec A \times \vec B = \vec B \times \vec A$
3. c $\vec B \times \vec A = -\vec A \times \vec B$
4. d $\vec A \cdot \vec B = \vec B \cdot \vec A$

Which vector should be added to the sum of the vectors $(\hat\imath - 2\hat\jmath + 2\hat k)$ and $(2\hat\imath + \hat\jmath - \hat k)$ so that the resultant vector is a unit vector along the x-axis?

1. a $(2\hat\imath + 4\hat\jmath - \hat k)$
2. b $(-2\hat\imath + \hat\jmath - \hat k)$
3. c $(2\hat\imath - \hat\jmath - \hat k)$
4. d $(-2\hat\imath - \hat\jmath - \hat k)$

If $\vec A$ and $\vec B$ are two vectors with an angle $\theta$ between them, then the value of $\vec A \cdot (\vec A \times \vec B)$ is:

1. a $A^2B$
2. b $A^2B\sin\theta$
3. c $A^2B^2\sin\theta$
4. d Zero

If the angular velocity of a particle is $\vec\omega = (3\hat\imath - 4\hat\jmath + \hat k)$ and its position vector is $\vec r = (5\hat\imath - 6\hat\jmath + 6\hat k)$, then its linear velocity $\vec v$ will be:

1. a $(6\hat\imath + 2\hat\jmath - 3\hat k)$
2. b $(-18\hat\imath - 13\hat\jmath + 2\hat k)$
3. c $(4\hat\imath - 13\hat\jmath + 6\hat k)$
4. d $(6\hat\imath - 2\hat\jmath + 3\hat k)$

Two forces $\vec F_1$ and $\vec F_2$ are acting on a particle with magnitudes of 5 dyne and 10 dyne respectively. The magnitude of the resultant force can be:

1. a 12 dyne
2. b 5 dyne
3. c 4 dyne
4. d 8 dyne

If $\vec P + \vec Q = \vec R$ and $P^2 + Q^2 = R^2$, then the angle between $\vec P$ and $\vec Q$ will be:

1. a $0$
2. b $\pi/4$
3. c $\pi/2$
4. d $\pi$

Three vectors $\vec P$, $\vec Q$ and $\vec R$ are such that $|\vec P| = |\vec Q|$, $|\vec R| = \sqrt{2}\,|\vec P|$ and $\vec P + \vec Q + \vec R = 0$. What are the angles between $\vec P$ and $\vec Q$, $\vec Q$ and $\vec R$, and $\vec P$ and $\vec R$?

The position of a particle is given by $\vec r = 3.0t\,\hat\imath - 2.0t^2\,\hat\jmath + 4.0\,\hat k$ m, where $t$ is in seconds and the coefficients have proper units for $\vec r$ to be in metres. (a) Find the velocity $\vec v$ and acceleration $\vec a$ of the particle. (b) What is the magnitude and direction of the velocity of the particle at $t = 2.0$ s?

A particle starts from the origin at $t = 0$ s with a velocity of $10.0\,\hat\jmath$ m/s and moves in the xy-plane with a constant acceleration of $(8.0\,\hat\imath + 2.0\,\hat\jmath)$ m s$^{-2}$. (a) At what time is the x-coordinate of the particle 16 m? (b) What is the y-coordinate of the particle at that time? (c) What is the speed of the particle at that time?

If the sum of two unit vectors is a unit vector, what is the magnitude of their difference?