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I am having difficulty figuring out how to proceed with this problem. Any help demonstrating the expression of the vector for each respective triangle would be greatly appreciated.

Express vector x and vector y in terms of vector u , vector v and vector w .

Let me denote vectors with an uppercase letter, so that we want X and Y in terms of U, V and W.

a) It looks like X + U = -V, so that X = -(U + V). The minus sign comes from the fact that V is drawn as pointing away from the end of U towards the beginning of X.

b) U + X = V so X = V - U

Y = U + W.

c) Let the vector joining the end of U to the end of W be Q. Then U + Q = W. Since X hits the middle of Q, X = U +(1/2)Q = U +(1/2)(W - U) = (1/2)(W + U). You can verify this by looking at how many units (squares) are needed vertically and horizontally to go from the point at the end of U to the end of X vs the end of W (half as many).

Stringing the vectors together, W + V + Y = U so that Y = U - W - V.

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