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GB-34-03-001 · Position vector dividing a line

In triangle OAB, OA→=a\overrightarrow{OA}=\mathbf a and OB→=b\overrightarrow{OB}=\mathbf b. P lies on AB with AP : PB = 11 : 7. Find OP→\overrightarrow{OP}.

Vectors: Route & Ratio Division on a Line Booklet p. 90
Method
1) Write route AB = AO + OB = −a + b
2) Write OP = OA + fraction × AB
3) Expand and collect a and b terms
Worked Example (GB-34-03-001)
1)
AB→=b−a\overrightarrow{AB}=\mathbf b-\mathbf a
2)
Use OP→=a+1118(b−a)\overrightarrow{OP}=\mathbf a+\frac{11}{18}(\mathbf b-\mathbf a)
3)
718a+1118b\frac{7}{18}\mathbf a+\frac{11}{18}\mathbf b
Ans = 718a+1118b\frac{7}{18}\mathbf a+\frac{11}{18}\mathbf b