Oabc is a tetrahedron and oa=a, ob=b, and oc=c. the point p and q are such that oa =ap and 2ob = bq. the point m is a midpoint of pq. find (i)ab (ii)pq (iii)cq (iv)qm (v)mb (vi)om in terms of a, b, and c.

Solution:

Let OA=a, OB=b, and OC=c

Then OP=2a and OQ=3b

OA+AB=OB ⇒ AB=b-a

OP+PQ=OQ ⇒ PQ = 3b-2a

OC+CQ = OQ ⇒ CQ = 3b-c

(i) AB = b-a

(ii) PQ = 3b-2a

(iii) CQ = 3b-c

(iv) QM =

(v) MB =  

(vi) OM =

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step-by-step explanation:

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step-by-step explanation: