Vectors Proof Questions

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Question 1
Medium

A vector diagram showing a triangle OAB. Vector OA is labeled 'a' and vector OB is labeled 'b'.

OA⃗=a \vec{OA} = \mathbf{a} OA=a OB⃗=b \vec{OB} = \mathbf{b} OB=b

P P\,P is the point on AB AB\,AB such that AP:PB=1:4AP:PB = 1:4AP:PB=1:4

OP⃗=k(4a+b) \vec{OP} = k(4\mathbf{a} + \mathbf{b}) OP=k(4a+b)

Find the value of kkk.

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