Given $A = 3\hat{i} + 4\hat{j}$ and $B = 7\hat{i} + 24\hat{j}$,find a vector that has the same magnitude as $B$ and is parallel to $A$.

Which of the following colours of visible light has the lowest energy?

$A$ 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 $t = 2 \, s$?

State with reasons,whether the following algebraic operations with scalar and vector physical quantities are meaningful:
$(a)$ adding any two scalars,
$(b)$ adding a scalar to a vector of the same dimensions,
$(c)$ multiplying any vector by any scalar,
$(d)$ multiplying any two scalars,
$(e)$ adding any two vectors,
$(f)$ adding a component of a vector to the same vector.

$A$ force,$\vec{F}=(4 \hat{i}+3 \hat{j}-5 \hat{k}) \text{ N}$,is acting on a body. If the horizontal direction is taken along the $\hat{i} + \hat{j}$ direction,find the angle $\theta$ that the force makes with this horizontal direction.

If water at $100^\circ C$ cools in $10$ minutes to $80^\circ C$ and to $65^\circ C$ in the next $10$ minutes, then the room temperature will be ...