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# Vectors problem

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Let $$\mathbf{x}$$ and $$\mathbf{y}$$ be two perpendicular unit vectors.

(a) Find a formula for the magnitude of an arbitrary linear combination $$a\mathbf{x} + b\mathbf{y}$$ of $$\mathbf{x}$$ and $$\mathbf{y}$$ in terms of $$a$$ and $$b$$.

(b) Find the precise condition on $$a, b, c$$ and $$d$$ under which the linear combinations $$a\mathbf{x} + b\mathbf{y} \text{ and } c\mathbf{x} + d \mathbf{y}$$ are perpendicular.

Feb 2, 2022