If $A = 3\hat i + 4\hat j$ and $B = 7\hat i + 24\hat j,$ the vector having the same magnitude as $B$ and parallel to $A$ is

What is the magnitude of a new vector obtained by multiplying a vector $\vec{A}$ by $-\frac{3}{2}$?

Two vectors $\overrightarrow{X}$ and $\overrightarrow{Y}$ have equal magnitude. The magnitude of $(\overrightarrow{X}-\overrightarrow{Y})$ is $n$ times the magnitude of $(\overrightarrow{X}+\overrightarrow{Y})$. The angle between $\overrightarrow{X}$ and $\overrightarrow{Y}$ is:

The resultant of two vectors $A$ and $B$ makes an angle $\alpha$ with $A$ and $\beta$ with $B$. Which of the following is correct?

A body cools from $100^\circ C$ to $60^\circ C$ in $20$ minutes, the temperature of the surroundings being $20^\circ C$. The total time taken (in minutes) for the body to cool down to $40^\circ C$ is ...

Vector $\overrightarrow{A}$ makes equal angles with $x, y,$ and $z$ axes. The value of its components (in terms of the magnitude of $\overrightarrow{A}$) will be: