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. 

A car travels at an average speed of $40 \mathrm{km}/\mathrm{hr}$. After travelling east for $1 \mathrm{hr}$ it turns and travels north for $45 \min$ then east again for $30 \min$. Find its displacement.

Calculate the vector sum of two unit vectors.

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?

Six vectors, a through f​ have the magnitudes and directions indicated in the figure. Which of the following statements is true?

The vectors $\overrightarrow{P}=2\hat{i}+p\hat{j}+q\hat{k}$ and $\overrightarrow{B}=5\hat{i}+7\hat{j}+3\hat{k}$ are parallel to each other. The values $p$ and $q$ are respectively

A bus is going due north at a speed of $50 \mathrm{km}/\mathrm{h}$. It makes $90°$ left turn without changing its speed. The change in the velocity of the bus is

How do you know if vectors are anti-parallel?

Which one of the following physical quantities is not a fundamental quantity?

Physical quantities are classified into two types. There are fundamental and derived quantities.

Define physical quantity ?

The vectors $\overrightarrow{A}$ and $\overrightarrow{B}$ are two mutually perpendicular vectors. Their dot product remains the same when the magnitude of $\overrightarrow{A}$ becomes three times its previous value.

The product of a vector $\overrightarrow{A}$ and a real number $R$ is a vector$R\overrightarrow{A}$ . The direction of vector $R\overrightarrow{A}$ may be opposite to the direction of vector $\overrightarrow{A}$.

Scalar quantity definition

Mass - 12 Kg +5 kg = _____