Liner algebra/ how to do this question (vector geometry)

[chacha2801]

Let v be a vector (in R2 or R3) and let d be a nonzero vector. Prove that projd v is orthogonal

to v -projd v.

 

[Deleted member 4993]

Let v be a vector (in R2 or R3) and let d be a nonzero vector. Prove that projd v is orthogonal to v -projd v.

Please show us what you have tried and exactly where you are stuck.

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[Dr.Peterson]

Let v be a vector (in R2 or R3) and let d be a nonzero vector. Prove that projd v is orthogonal

to v -projd v.

Start by telling us the definition you were given for proj_d(v). The proof will be very different depending on whether, for instance, you have a geometric definition or a formula to define it.

Then think about how to prove that two vectors are orthogonal. One way would involve the dot product.