Motion in plane practice · Medium

If $a^2+b^2+c^2=1$ where $a, b, c \in R$, then the maximum value of $(4 a-3 b)^2+(5 b-4 c)^2+(3 c-5 a)^2$ is

Two vectors $\vec{A}$ and $\vec{B}$ are such that $\vec{A}+\vec{B}=\vec{C}$ and $A^2+B^2=C^2$. Which of the following statements is correct?

A: Two row boats moving parallel to each other and nearby, are attracted towards each other
R: Increase of velocity of fluid flow decrease the pressure

The vector $\hat{\mathbf{i}}+\mathrm{x} \hat{\mathbf{j}}+3 \hat{\mathrm{k}}$ is rotated through an angle $\theta$ and doubled in magnitude, then it becomes $4 \hat{i}+(4 x-2) \hat{j}+2 \hat{k}$. The possible positive value of $x$ is

A boat takes two hours to travel 8 km and back in still water. If the velocity of water 4 $\mathrm{km}{\mathrm{h}^{ - 1}}$, the time taken for going ups tream 8km and coming back is

A ball is projected with velocity ${v_0}$ at an angle of elevation ${30^0}$. Mark the correct statement

Consider a vector $\overrightarrow F = 4\widehat i - 3\widehat j$. Another vector that is perpendicular to $\overrightarrow F$ is

What is the unit vector along $\hat i + \hat j\,\,?$

IF $\overrightarrow u = a\widehat i + b\widehat j + c\widehat k\,\,with\,\hat i,\hat j,\hat k$ are in east, north and vertical directions, horizontal component of velocity of projectile is

Statement-I: If dot product and cross product of $\vec{a}$ and $\vec{b}$ are zero, it implies that one of the vector $\vec{a}$ and $\vec{b}$ must be a null vector.
Statement-II: Null vector is a vector with zero magnitude.

A stone is projected from the ground with velocity $50\mathrm{\;m}{\mathrm{s}^{ - 1}}$ and angle of ${30^0}$. It crosses a wall after 3 s. How far beyond the wall the stone will strike the ground?

Vector $\vec A$ has magnitude of 5 unit directed along east, then vector $6\vec A$

Statement-I: Finite angular displacement is not a vector quantity.
Statement-II: It does not obey the laws of vector addition.

The angle between the vectors $(\overrightarrow i + \overrightarrow j + \overrightarrow k )$ and $(\overrightarrow i - \overrightarrow j - \overrightarrow k )$ is

Two boys $P$ and $Q$ are playing on a river bank. $P$ plans to swim across the river directly and come back. $Q$ plans to swim downstream by a length equal to the width of the river and then come back. Both of them bet each other, claiming that the boy succeeding in less time will win. Assuming the swimming rate of both $P$ and $Q$ to the same, it can be concluded that

A vector $\overrightarrow A$ points vertically upward and $\overrightarrow B$ points towards north. The vector product of $\overrightarrow A \, \times \,\overrightarrow B$ is

Assertion : If a body of mass m is projected upwards with a speed V making an angle $\theta$ with the vertical, than the change in the momentum of the body along X–axis is zero.
Reason : Mass of the body remains constant along X–axis.

Two bullets are fired simultaneously, horizontally and with different speeds from the same place. Which bullet will hit the ground first?

If the resultant of two forces $\left( {A + B} \right)\,and\,\left( {A - D} \right)\,is\,\sqrt {{A^2} + {B^2}}$ , then the angle between these forces is

The maximum horizontal range of a projectile is 400 m. The maximum value of the height attained by it will be

The time of flight of a projectile on an upward inclined plane depends upon

The vector that must be added to the vector $\widehat i - 3\widehat j + 2\widehat k\,and\,3\widehat i + 6\widehat j - 7\widehat k$ so that the resultant vector is a unit vector along the y-axis is

What is the angle between $(\overrightarrow{\mathrm{P}}+\overrightarrow{\mathrm{Q}})$ and $(\overrightarrow{\mathrm{P}} \times \overline{\mathrm{Q}})$

For angle $\ldots X \ldots$ the projectile has maximum range and it is equal to ...X.... Here, $\mathrm{X}$ and $\mathrm{Y}$ refer to

Given $\mathrm{\vec A} = \hat i + 2\hat j - 3\hat k$. When a vector $\mathrm{\vec B}$ is added to $\mathrm{\vec A}$, We get a unit vector along X=axis. Then,$\mathrm{\vec B}$ is

The plane which can be formed with the vectors $\overrightarrow a = 3\overrightarrow i - 4\overrightarrow j + 2\overrightarrow k$,$\overrightarrow b = 2\overrightarrow i - \overrightarrow j - 6\overrightarrow k ,\overrightarrow c = 5\overrightarrow i - \overrightarrow {5j} - 4\overrightarrow k$ IS