If $0.5 \hat{i} + 0.8 \hat{j} + c \hat{k}$ is a unit vector, then $c$ is

$A$ mosquito is moving with a velocity $\overrightarrow{v} = 0.5t^2 \hat{i} + 3t \hat{j} + 9 \hat{k} \, m/s$. What will be the direction of the mosquito after $t = 2 \, s$?

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 ...

$A$ unit vector is represented as $(0.8 \hat{i} + b \hat{j} + 0.4 \hat{k})$. Hence,the value of $b$ must be:

If $\vec{A} + \vec{B} = \vec{C}$ and $|\vec{A}| + |\vec{B}| = |\vec{C}|$,what can be said about the direction of these vectors?

Can you associate vectors with $(a)$ the length of a wire bent into a loop,$(b)$ a plane area,$(c)$ a sphere? Explain.