What is the position vector of a particle located at $(3, 2, 5)$?

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

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.

If the angle between $\hat{a}$ and $\hat{b}$ is $60^{\circ}$,then which of the following vector$(s)$ have magnitude one?

Let $\overrightarrow{A} = \hat{i}A\cos\theta + \hat{j}A\sin\theta$ be any vector. Another vector $\overrightarrow{B}$ which is normal to $\overrightarrow{A}$ is

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