# To find inner product in vector spaces

Find each of the following for the given inner product defined in R^2

a) d(u,v)

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)

https://brainmass.com/math/vector-calculus/find-inner-product-vector-spaces-244917

#### Solution Preview

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 ...

#### Solution Summary

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.

$2.19