Let x=(1,1,1,1)^T and y=(8,2,2,0)^T (a) Determine the angle theta between x and y (b) find the vector projection p of x onto y (c) verify that x-p is orthognal to p (d) compute ||x-p||, ||p||, ||x|| and verify that the pythagorean law is satisfied

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A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

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A: Note that : Curl of the vector field describes it's rotation.

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A: Here we have to find orthogonal projection of y onto u and also we have to calculate distance d.

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A: Given (a)  The component of u along v is the scalar |u| cos θFormula: u·v=|u||v|   cos θ

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A: According to bartleby guidelines we supposed to do the first one of multiple questions kindly repost…

Q: find the projection of v onto u.

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A: To solve this problem we follow the following steps : Finding image :  Write down the given…

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A: Due to Bartleby answering guidelines I have solved only first three Subparts of the given question…

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A: Note:  Since you have posted multiple questions, we will solve first question for you. Kindly repost…

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