In Rectangular Components of a Vector in Three Dimensions why vector of OR = vector of OS + OP + TR please explain?

Refer to the figure given above:

In triangle ORT,

Using triangle law of addition,

=> OR = OT + TR  ......(i)

In parallelogram OSTP,

Using parallelogram law of addition,

=> OT = OP + OS  .....(ii)

Substituting the value of OT  in equation (i)

=> OR = OP + OS + TR

Also, TR = OQ

 

=> OR = OP + OS + OQ

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