vector question, BP,PC,AB,AC,AP are all vectors
A, B, C are vertices of a triangle with a point P on the side of BC. Given that 3BP =4PC, find k if 3AB+ 4AC= kAP

Question

vector question, BP,PC,AB,AC,AP are all vectors
A, B, C are vertices of a triangle  with a point P on the side of BC. Given that 3BP =4PC, find k if 3AB+ 4AC= kAP

amistre64 · Answer

might help to draw out the triangle ....

amistre64 · Answer

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amistre64 · Answer

AC = AB + BP + PC
AP = AB + BP

3AB+ 4AB + 4BP + 4PC= kAB + kBP

3AB - kAB  + 4AB =  kBP - 4BP - 4PC

3AB - kAB  + 4AB =  kBP - 4BP - 3BP

7AB - kAB =  kBP -7BP

(7-k)AB =  (k-7)BP

those are just some ideas that come to mind ...