(Expressing a vector as a linear combination of two other ve
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(Expressing a vector as a linear combination of two other vectors with which it is coplanar) Suppose that u, v, and r ar
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(Expressing a vector as a linear combination of two other vectors with which it is coplanar) Suppose that u, v, and r are position vectors of points U, V , and P, respectively, that u is not parallel to v, and that P lies in the plane containing the origin, U, and V . Show that there exist numbers and such that r D u C v. Hint: Resolve both v and r as sums of vectors parallel and perpendicular to u as suggested in Exercise 31.
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