Motion in plane practice · Easy

The angle made by the vector $A = \hat i + \hat j$ with x – axis is

Unit vector

I. has dimensions and a unit.

II. when multiplied by a scalar quantity, it results a scalar.

Which of the following statement(s) is/are incorrect?

Identify the vector quantity among the following

A particle is projected at an angle of ${60^0}$ above the horizontal with a speed of $10\mathrm{\;m}{\mathrm{s}^{ - 1}}$. After some time the direction of its velocity makes an angle of ${30^0}$ above the horizontal. The speed of the particle at this instant is

If $\mathbf{A}$ and $\mathbf{B}$ are two non-zero vectors having equal magnitude, the angle between the vectors $\mathbf{A}$ and $\mathbf{A}-\mathbf{B}$ is

If $\frac{1}{{\sqrt 3 }}\left| {\vec a \times \vec b} \right| = \overrightarrow a \cdot \overrightarrow b$ then angle between $\overrightarrow a$ and $\overrightarrow b$ is

Two projectiles thrown at $30^{\circ}$ and $45^{\circ}$ with the horizontal respectively, reach the maximum height in same time. The ratio of their initial velocities is:

The angle between the two vectors $\vec A\, = \,5\hat i\, + \,5\hat j$ and $\vec B\, = \,5\hat i\, - \,5\hat j$ will be

Given two vector $\bar A = 2i + 6j + 4k$ and $\bar B = i - 2j + 8k$. The magnitude of their resultant is

The horizontal range is four times the maximum height attained by a projectile. The angle of projection is

If $\frac{1}{{\sqrt 3 }}\left| {\vec a \times \vec b} \right| = \overrightarrow a \cdot \overrightarrow b$ then angle between $\overrightarrow a$ and $\overrightarrow b$ is

If vectors $\bar A = 2i + 3j + Pk$ and $\bar B = 3\bar i - 8\bar j + 2\bar k$ are perpendicular to each other. Then value of $P$ is

If the magnitude of resultant of two vectors is equal to magnitude of either vectors, then angle between them is

The component of a vector along any other direction is

The value of $\left( {\bar A + \bar B} \right) \times \left( {\bar A - \bar B} \right)$ is

Angle (in rad) made by the vector $\sqrt 3 i + j$ with the x-axis is

Vector $\bar A = 4i + 2j - 3k,\,\,\bar B = 5\bar i + \bar j - 2\bar k$ and $\bar C = 3i - j + 2k$. Then $\bar A.\left( {\bar B \times \bar C} \right)$ is

Assertion If a particle is projected vertically upwards with velocity $u$, the maximum height attained by the particle is $h_1$. The same particle is projected at angle $30^{\circ}$ from horizontal with the same speed $u$. Now the maximum height is $h_2$. Thus, $h_1=4 h_2$.

Reason In first case, $v=0$ at highest point and in second case, $v \neq 0$ at highest point.

Component of the vector $\mathbf{A}=2 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}$ along the vector $\mathbf{B}=(\hat{\mathbf{i}}+\hat{\mathbf{j}})$ is

Assertion: The angle between the two vectors $(\hat{i}+\hat{j})$ and $(\hat{i}+\hat{k})$ is $\frac{\pi}{3}$ radian.
Reason: Angle between two vectors $\vec{A}$ and $\vec{B}$ is given by $\theta=\cos ^{-1}\left(\frac{\vec{A} \cdot \vec{B}}{A B}\right)$.

Two bodies are projected with the same velocity. If one is projected at an angle of $30^\circ$ and the other at angle of $60^\circ$ to the horizontal, the ratio of the maximum heights reached is

The resultant of $A\,\, \times \,\,0$ will be equal to

I. Displacing a vector parallel to itself leaves the vector unchanged.

II. Three equal vectors cannot add upto zero.

Which of the following statement(s) is/are correct?

If two vectors $\overline A = 2\overrightarrow i - 2\overrightarrow j + \overrightarrow k$, and $\overline B = 2\overrightarrow i + 6\overrightarrow j - m\overrightarrow k$ are perpendicular to each other than the value of $m$ is

The position vector $\bar r$ of a particle is given by $\bar r = \left( {A\sin \omega t} \right)i + \left( {A\cos \omega t} \right)j$. If $v$ is velocity of particle. Then $\bar v.\,\bar r =$

When a projectile is fired at an angle $\theta$ wrt. horizontal with velocity $u$, then its vertical component

If two directional cosine of a vectors are $\frac{1}{{\sqrt 2 }}$ and $\frac{1}{{\sqrt 3 }}$ then the value of third directional cosine is

Two forces of 12 N and 8 N act upon a body. The resultant forces on the body has maximum value of

The two forces are in the ratio of 2:5 maximum and minimum of their resultant are in the ratio of

Which of the following not a vector quantity?