The vector that must be added to the vector $\hat i - 3\hat j + 2\hat k$ and $3\hat i + 6\hat j - 7\hat k$ so that the resultant vector is a unit vector along the $y-$axis is
Magnitudes of two vector $\overrightarrow A $ and $\overrightarrow B $ are $4$ units and $3$ units respectively. If these vectors are $(i)$ in same direction $(\theta = 0^o).$ $(ii)$ in opposite direction $(\theta = 180^o)$, then give the magnitude of resultant vector.
Assertion $A$ : If $A, B, C, D$ are four points on a semi-circular arc with centre at $'O'$ such that $|\overrightarrow{{AB}}|=|\overrightarrow{{BC}}|=|\overrightarrow{{CD}}|$, then $\overrightarrow{{AB}}+\overrightarrow{{AC}}+\overrightarrow{{AD}}=4 \overrightarrow{{AO}}+\overrightarrow{{OB}}+\overrightarrow{{OC}}$
Reason $R$ : Polygon law of vector addition yields $\overrightarrow{A B}+\overrightarrow{B C}+\overrightarrow{C D}+\overrightarrow{A D}=2 \overrightarrow{A O}$
In the light of the above statements, choose the most appropriate answer from the options given below
If the sum of two unit vectors is also a unit vector. then magnitude of their difference and angle between the two given unit vectors is ..............
Two forces of magnitude $8 \,N$ and $15 \,N$ respectively act at a point. If the resultant force is $17 \,N$, the angle between the forces has to be .......