Let X and Y be points in R³. Let P be a point on the line segment joining X and Y such that the distance XP is three times the distance YP. What is the position vector P in terms of the position vectors X and Y? (Use syntax like (-1/2)*X + (1/2)*Y .)

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A: Firstly we hae to apply translation then reflection and then find the new point.

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Q: PLease don't provide handwritten solution.

A: Step 1: Given that, u=[3,4,−5]v=[0,−6,4] To find w=2u−3v ,we first need to compute the scalar…

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A: if a vector is of the form  a→=a1,a2  then a→=a12+a22 see  below the answer

Q: M] - [8] x+y -3x+y.

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A: topic - vectors

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A: Solution (11.)

Q: ,1), (2, 2), (1, 3), (4, 1), (3, 2), (2, 3), (1,4), (5, 1), .... Show that this constitutes a proof…

A: We will answer the first question only as we don't answer multiple questions at a time. Please…

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