b) Verify that the following is an inner product on R² where u = (x1, x2) , v = (yı, Y2) f(u, v) = x,Y1 – 2x1Y2 – 2x,y1 + 5x2Y2 Also explain whether inner product of two vectors is same as the usual product of two vectors. i) ii) If u = (2,3) , v = (1, 5), then find inner product of u, v by using above product . Normalize the vectors u, v.

Q: ex/IF Ā=i-j+3k and B =2 i+6j+3K Find the vector pricâ+B) and Prj (À-B).

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Q: Find F‘(0)  for the function f(x)=3xe5x b) Given vectors a=(1,3,-2) and b=(1,1,2) , find  3a +2b…

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A: To Define: Scalar Triple Product for vectors u, v and w in ℝ3.

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Q: Q1: You have the following vectors: U= 6 2 4 V= 3 -2 3 0 3 W = -4 Z- 2 2 2 Which of the vector…

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Q: Let V1 = 2 V2 = 0 2 V3 = 2 V4 = 3 Decide the dependence or independence of the vectors {V₁, V2, V₁}…

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Q: i) Express the vector u in terms of a, b, c a b p u C

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Q: (b) If u and v are vectors in R' such that ||ū|| = 1 and |||| = 2 then u · i# 10.

A: The angle between two vectors and Dot product in R3 is related by