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 sum of the magnitudes of two forces acting at point is 18 and the magnitude of their resultant is 12. If the resultant is at 90° with the force of smaller magnitude, what are the, magnitudes of forces?

Can the resultant of 2 vectors be zero ?

If the resultant of $\mathrm{n}$forces of different magnitudes acting at a point is zero, then the minimum value of $\mathrm{n}$ is $3.$

What are the conditions for linear independence of vectors?

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.

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

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.

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

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

The resultant $R$ of $P$ and $Q$ is perpendicular to $P$. Also $\left|P\right|\mathit{=}\left|R\right|$. The angle between $P$ and $Q$ is 

How many minimum numbers of vectors of unequal magnitudes are required to give zero resultant?

The square of resultant of two equal forces is three times their product. Angle between the forces is

Let the vectors $\overrightarrow{PQ}, \overrightarrow{QR}, \overrightarrow{RS}, \overrightarrow{ST}, \overrightarrow{TU}$ and $\overrightarrow{UP}$ represent the sides of a regular hexagon.

Statement I: $\overrightarrow{PQ}\times \left(\overrightarrow{RS}+\overrightarrow{ST}\right)\ne \overrightarrow{0}$

Statement II: $\overrightarrow{PQ}\times \overrightarrow{RS}=\overrightarrow{0}$ and $\overrightarrow{PQ}\times \overrightarrow{ST}\ne \overrightarrow{0}$