How Do You Solve Vector Problems in Triangle Geometry?

[dagg3r]

Vector Gah!

Vector questions. Need help on these three.

In ∆OAB, OA = a and OB = b. P is a point on AB such that BP:PA 1:2.
Q is a point on the extension of OP such that OQ = 1.5OP

a) Express BP and OP in terms of ‘a’ and ‘b’.
these are the answers but how do they get it?
BP = (1/3)(a - b)
OP = (1/3)(a + 2b)

b) Show that AQ = -0.5a + b
i have no idea how to prove this


c) Given that BQ = kOA, find the value of k.
once again this is the answer but i don't know how to approach this can someone show me how to get this value thanks
k = 0.5

 

[Galileo]

Draw the vector that define the triangle. One side is made by the vector a, the other by b and the third by a-b. Then draw the points P and Q. From the drawing you can see that BP is one third the vector (a-b). The others are done similarly.