Addition and Subtraction of 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:

The angle made by $\overrightarrow{r}=3\hat{\mathrm{i}}+3\hat{\mathrm{j}}$ with the $x$ axis is

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.

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 $\left(\stackrel{\rightharpoonup }{V_1}\right) +\left(\stackrel{\rightharpoonup }{V_2}\right)$.

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

Out of the following set of forces, the resultant of which cannot be zero ?

When the angle between the vector $\overrightarrow{a}$ and $\overrightarrow{b}$ is $\theta$, their resultant is $5\sqrt{a^2+b^2}$. When the angle is $\left(90°-\theta \right)$ the resultant is $3\sqrt{a^2+b^2}$. In this condition $\tan \theta$ is

The component of $9\hat{\mathrm{i}}+17\hat{\mathrm{k}}$ along $\mathrm{z}$ -axis is:

The component of a vector is

Two forces of equal magnitude act, simultaneously, on a particle. If the magnitude of their resultant is equal to either of them, angle between them is

If a vector $\overrightarrow{P}$ making the angles $\mathrm{\alpha }, \mathrm{\beta }$ and $\mathrm{\gamma }$, respectively, with $X, Y$ and $Z$ axes, then ${\sin }^2\mathrm{\alpha }+{\sin }^2\mathrm{\beta }+{\sin }^2\mathrm{\gamma }=$

$\overrightarrow{A}$ 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 $2 \hat{i}+3 \hat{j}+4 \hat{k}$.

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