In C[0,1], with inner product defined by (3), consider the vectors 1 and x.

Find the angle theta between 1 and x.

(3)$\displaystyle \int_{0}^{1}f(x)g(x)dx$

Find the angle theta between 1 and x

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- Mar 26th 2010, 08:19 PMdwsmithAngle between 1 and x
In C[0,1], with inner product defined by (3), consider the vectors 1 and x.

Find the angle theta between 1 and x.

(3)$\displaystyle \int_{0}^{1}f(x)g(x)dx$

Find the angle theta between 1 and x - Mar 26th 2010, 11:16 PMPulock2009didnot understand
- Mar 26th 2010, 11:17 PMDrexel28
- Mar 27th 2010, 03:30 AMHallsofIvy
You are thinking of C[0,1] as an inner product space with the standard inner product $\displaystyle <f, g>= \int_0^1 f(x)g(x)dx$.

Of course, in any inner product space, $\displaystyle <u, v>= |u||v|cos(\theta)$ where $\displaystyle \theta$ is the angle between u and v.

The particular calculation for the angle between u= 1 and v= x should be easy. - Mar 27th 2010, 10:27 AMdwsmith
After taking the integral, I obtain 1/2. How does that help me obtain the angle of pi/6?

- Mar 27th 2010, 11:07 AMHallsofIvy
After taking

**what**integral? The formula I gave you, $\displaystyle <u, v>= |u||v|cos(\theta)$ requires**three**integrals to determine <u, v>, |u|, and |v|.