Question

What is Hexagonal law of vector addition??

Answer 1

Answer:

Since the hexagon is a regular Hexagon, the Resultant of the given vectors will be zero, as per the polygon law of vector addition, if they are arranged in a head to tail formation in any closed polygon. Since the head of the last vector is joined with the tail of the first vector, their Resultant is zero..

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Explanation:

Answer 2

Answer:

"According to law of hexagonal, if sides of hexagonal represents the magnitude of vectors then closing side of hexagon represent the resultant".

So,

$\sf{In\: \triangle\: OAB}$

$\sf{\overrightarrow{OB}=\overrightarrow{OA}+\overrightarrow{AB}\:\:\:\:.....[From\: Triangles\: law\: of\: vector\: addition]}$

$\sf{\overrightarrow{OB}=\overrightarrow{P}+\overrightarrow{Q}\:\:\:\:......(1)}$

Similarly,

$\sf{In\: \triangle\: OBC}$

$\sf{\overrightarrow{OC}=\overrightarrow{OB}+\overrightarrow{BC}}$

$\sf{\overrightarrow{OC}=(\overrightarrow{P}+\overrightarrow{Q})+\overrightarrow{R}\:\:\:\:.....(2)}$

$\sf{In\: \triangle\: OCD}$

$\sf{\overrightarrow{OD}=\overrightarrow{OC}+\overrightarrow{CD}}$

$\sf{\overrightarrow{OD}=(\overrightarrow{P}+\overrightarrow{Q}+\overrightarrow{R})+\overrightarrow{S}\:\:\:\:.....(3)}$

$\sf{In\: \triangle\: OED}$

$\sf{\overrightarrow{OE}=\overrightarrow{OD}+\overrightarrow{DE}}$

$\sf{\overrightarrow{OE}=(\overrightarrow{P}+\overrightarrow{Q}+\overrightarrow{R}+\overrightarrow{S})+\overrightarrow{T}\:\:\:\:.....(4)}$

$\sf{So,\: \overrightarrow{OE}\: represents\: the\: resultant.}$

${\boxed{\boxed{\sf{\overrightarrow{OE}=\overrightarrow{P}+\overrightarrow{Q}+\overrightarrow{R}+\overrightarrow{S}+\overrightarrow{T}}}}}$