Question

The three vectors `vec A, vec B and vec C` are repesented in magnitude and direction by `vec (OP , vec (OQ),` show that (S) is the mid point of ` (PQ).
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Answer 1

In ` Delta OPS`, by vectors addition,
` vec (OS) =vec (OP) + vec (OS)` ….(i)
Similarly, in ` Delta OQS`, we have
` vec (OS) =vec (OQ)+ vec (QS)` …(ii)
Adding (i) and (ii), we have
` 2 vec (OS) = vec (OP) + vec (OQ) + vec (PS) + vec (QS)`
or ` vec C = vec A + vec B + vec (PS) + vec (QS)`
or ` (2 vec C - vec A - vec B) = vec (PS) + vec (QS)`
or ` 0= vec (PS) + vec (QS) (:. 2 vec C = vec A + vec B)`
or ` vec (PS) =- vec (QS)` .
So, (S) is the mid point of (PQ)`