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Suppose that a and b are nonzero vectors. (a) Under what circumstances is comp_ $\mathbf{b}=\mathrm{comp}_{\mathbf{b}}$ a? (b) Under what circumstances is proja $...

Question

Suppose that a and b are nonzero vectors. (a) Under what circumstances is comp_ $\mathbf{b}=\mathrm{comp}_{\mathbf{b}}$ a? (b) Under what circumstances is proja $\mathbf{b}=$ proj $\mathbf{b}$ a?

Suppose that a and b are nonzero vectors. (a) Under what circumstances is comp_ $\mathbf{b}=\mathrm{comp}_{\mathbf{b}}$ a? (b) Under what circumstances is proja $\mathbf{b}=$ proj $\mathbf{b}$ a?



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Suppose that $ a $ and $ b $ are nonzero vectors that are not parallel and $ c $ is any vector in the plane determined by $ a $ and $ b $. Give a geometric argument to show that $ c $ can be written as $ c = sa + tb $ for suitable scalars $ s $ and $ t $. Then give an argument using components


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