If the sum of two unit vectors is a unit vector, then magnitude of difference is

Two forces of $10 \,N$ and $6 \,N$ act upon a body. The direction of the forces are unknown. The resultant force on the body may be .........$N$

Given $a+b+c+d=0,$ which of the following statements eare 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 ?

In the cube of side $a$ shown in the figure, the vector from the central point of the face $ABOD$ to the central point of the face $BEFO$ will be

A body is at rest under the action of three forces, two of which are ${\vec F_1} = 4\hat i,\,{\vec F_2} = 6\hat j,$ the third force is

Two forces each numerically equal to $10$ $dynes$ are acting as shown in the adjoining figure, then the magnitude of resultant is.........$dyne$