$\vec{A}$ is a vector of magnitude $2.7$ units due east. What is the magnitude and direction of vector $4 \vec{A}$?

The component of a vector $P=3 \hat{i}+4 \hat{j}$ along the direction $(\hat{i}+2 \hat{j})$ is

$A$ physical quantity which has a direction:

State whether the following statements are true or false:
$(a)$ The unit vectors ${\hat i}$ and ${\hat j}$ along the $x$ and $y$-axes change with time.
$(b)$ If the angle between $\overrightarrow A$ and $\overrightarrow B$ is ${\theta _1}$ and the angle between $\overrightarrow A$ and $\overrightarrow C$ is ${\theta _2}$,then $\overrightarrow A \cdot \overrightarrow B = \overrightarrow A \cdot \overrightarrow C$ implies $\overrightarrow B = \overrightarrow C$.
$(c)$ The resultant vector of two coplanar vectors is also a coplanar vector.

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:

A body cools according to Newton's law of cooling from $100^\circ C$ to $60^\circ C$ in $20$ minutes. The temperature of the surroundings being $20^\circ C$, then the total time required for the body to cool down to $30^\circ C$ is