The value of a unit vector in the direction of vector $\vec A = 5\hat i - 12\hat j$ is:

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

If $A$ and $B$ are two vectors such that $|A + B| = 2|A - B|$,the angle between vectors $A$ and $B$ is:

Which of the following quantity/quantities are dependent on the choice of orientation of the co-ordinate axes?
$(a)$ $\vec{a}+\vec{b}$
$(b)$ $3a_x+2b_y$
$(c)$ $(\vec{a}+\vec{b}-\vec{c})$

The position vectors of points $A, B, C$ and $D$ are $A = 3\hat{i} + 4\hat{j} + 5\hat{k}$,$B = 4\hat{i} + 5\hat{j} + 6\hat{k}$,$C = 7\hat{i} + 9\hat{j} + 3\hat{k}$ and $D = 4\hat{i} + 6\hat{j}$. Then the displacement vectors $\overrightarrow{AB}$ and $\overrightarrow{CD}$ are:

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