Find each of the following for the given inner product defined in R^2
b) < u,v >
< u,v >=3u(subscript 1)v(subscript 1) + u(subscript 2)v(subscript 2)
where u=(-4,9) and v=(0,4)
According to the given formula for <u,v> one has <u,v> = 3 (-4)(0) + (9)(4)= 36. As for d(u,v) it is given by positive squre root of (u(subscript1) - (v(subscript 1))^2 +(u(subscript2) - (v(subscript2) ^2. Thus in the present case,one has d(u,v) = Positive ...
This problem explains how to find inner product of two vecotrs and also distance between them.There can be different formulas for defining an inner product of two vectors;here a particular formula has been used.