Two vectors $\overrightarrow{A}$ and $\overrightarrow{B}$ lie in a plane,and another vector $\overrightarrow{C}$ lies outside this plane. Then,the resultant of these three vectors,i.e.,$\overrightarrow{A} + \overrightarrow{B} + \overrightarrow{C}$:

For the resultant of two vectors to be maximum,what must be the angle between them? $(^o)$

Two vectors $A$ and $B$ are inclined at an angle $\theta$. Their resultant $R$ makes an angle $\phi$ with vector $A$. If the directions of $A$ and $B$ are interchanged,the resultant will have the same:

If the magnitude of a physical quantity is zero,can it be a vector? Give a suitable example.

Given $a+b+c+d=0,$ which of the following statements are correct:
$(a)$ $a, b, c,$ and $d$ must each be a null vector.
$(b)$ The magnitude of $(a+c)$ equals the magnitude of $(b+d)$.
$(c)$ The magnitude of $a$ can never be greater than the sum of the magnitudes of $b, c,$ and $d$.
$(d)$ $(b+c)$ must lie in the plane of $a$ and $d$ if $a$ and $d$ are not collinear,and in the line of $a$ and $d$ if they are collinear.

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 $A$.