Given that; $A = B = C$. If $\vec A + \vec B = \vec C,$ then the angle between $\vec A$ and $\vec C$ is $\theta _1$. If $\vec A + \vec B+ \vec C = 0,$ then the angle between $\vec A$ and $\vec C$ is $\theta _2$. What is the relation between $\theta _1$ and $\theta _2$ ?

Which of the following relations is true for two unit vectors $\hat{ A }$ and $\hat{ B }$ making an angle $\theta$ to each other$?$

If the magnitude of sum of two vectors is equal to the magnitude of difference of the two vectors, the angle between these vectors is ........ $^o$

Two forces are such that the sum of their magnitudes is $18\; N$ and their resultant is $12\; N$ which is perpendicular to the smaller force. Then the magnitudes of the forces are

Which of the following quantity/quantities are dependent on the choice of orientation of the co-ordinate axes?

$(a)$ $\vec{a}+\vec{b}$

$(b)$ $3 a_x+2 b_y$

$(c)$ $(\vec{a}+\vec{b}-\vec{c})$