Scalars and Vectors

A bus is moving on a straight road towards north with a uniform speed of  $50 \mathrm{km} {\mathrm{h}}^{-1}$  turns through  $90°$ anticlockwise. If the speed remains unchanged after turning , the increase in the velocity of bus in the turning process is:

If vectors $\overrightarrow{A}=\hat{\mathrm{i}}+3\hat{\mathrm{j}}+2\hat{\mathrm{k}}$ and $\overrightarrow{B}=3\hat{\mathrm{i}}+\hat{\mathrm{j}}+2\hat{\mathrm{k}}$ then find value of $\overrightarrow{A}\times \overrightarrow{B}$..

Convert the vector $\overrightarrow{r}=3\stackrel{\wedge }{i}+2\stackrel{\wedge }{j}$ into a unit vector.

When two right-angled vectors of magnitude $7 \mathrm{units} and 24 \mathrm{units}$ combine, what is the magnitude of their resultant?

The magnitude of the vector sum of two vectors is found to be equal to the sum of their magnitudes. 

If  $\left(\stackrel{\rightharpoonup }{V_1}\right) = 3\widehat{i } +4\widehat{j }+\hat{k} and \left(\stackrel{\rightharpoonup }{V_2}\right) = \widehat{i } -\widehat{j }-\hat{k}$then determine magnitude of $\left(\stackrel{\rightharpoonup }{V_1}\right) +\left(\stackrel{\rightharpoonup }{V_2}\right)$.

Vector $A$has a magnitude of $10$ units and makes an angle of $30°$ with the positive x-axis. Vector $B$ has a magnitude of $20$ units and makes an angle of $30°$ with the negative x-axis. What is the magnitude of the resultant between these two vectors?

$\overrightarrow{A}$ and $\overrightarrow{B}$ are two non-zero vectors inclined at an angle $\theta$, $\hat{\mathrm{a}}$ and $\hat{\mathrm{b}}$ are unit vectors along $\overrightarrow{A}$ and $\overrightarrow{B}$ respectively. The component of $\overrightarrow{A}$ in the direction of $\overrightarrow{B}$ is

Which of the following Cartesian coordinate systems is not followed in physics?

$\overrightarrow{\mathrm{A}}$ and $\overrightarrow{\mathrm{B}}$ are two vectors in a plane and $\overrightarrow{\mathrm{C}}$ is third vector perpendicular to the plane. Their resultant

The splitting of vectors into components is called

Two forces $F_1=1\mathrm{ }\mathrm{N}$ and $F_2=2\mathrm{ }\mathrm{N}$ act along the lines $x=0$ and $y=0$, respectively. Then the resultant of forces would be

Find the magnitude of the vector $2 \hat{i}+3 \hat{j}+4 \hat{k}$.

The unit vector $\left(a\hat{\mathrm{i}}+b\hat{\mathrm{j}}\right)$ is perpendicular to $\left(\hat{\mathrm{i}}+\hat{\mathrm{j}}\right).$ The value of ${}^{\text{'}}b^{\text{'}}$ is

The position vector of a particle is $\overrightarrow{r}=\left(a\cos \omega t\right)\hat{i}+\left(a\sin \omega t\right)\hat{j}$. The velocity vector of the particle is:

Select the correct alternative. The coordinates of a particle moving in a plane are given by $x=a \cos pt$ and $y=b \sin pt$ , where $a, b$ and $p$are positive constants of appropriate dimensions. Then:

The coordinates of a particle at time $t$ are $x=2t+4t^2$ and $y=5t$, where $x$ and $y$ are in metre and $t$ is in second. The acceleration of the particle at $t=5 s$ is :

A unit vector is represented as $\left(0.8\hat{\mathrm{i}}+b\hat{\mathrm{j}}+0.4\hat{\mathrm{k}}\right)$. The value of $b$ must be,

Find the magnitude of the vector $2 \hat{i}+3 \hat{j}+4 \hat{k}$.

The value of x for which $x.\left(\hat{\text{i}}+\hat{\text{j}}+\hat{k}\right)$ is a unit vector is