# Inner Product

Dustinsfl
Last two inner product questions.

The first one I am little confused on and the second one I don't know what to do.

See worked attached.

#### Attachments

• Untitled (1).pdf
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Staff Emeritus
Homework Helper

Dustinsfl
I don't know how to do it so I am confused on what to do.

Staff Emeritus
Homework Helper
If two vectors are orthogonal, what does that mean about their inner product? And what does it mean to say a vector is a unit vector?

Mentor
Last two inner product questions.

The first one I am little confused on and the second one I don't know what to do.

See worked attached.

For the first one, show that <cos(mx), sin(nx)> = 0. Also show that <cos(mx), cos(mx)> = 1 and that <sin(nx), sin(nx)> = 1.

For the second one, you're showing that the "1 norm" is a norm on Rn. Verify that the formula satisfies all the defining properties of a norm: positive definiteness, etc. BTW, this norm simply adds the absolute values of the coordinates of a vector. For example, in R3, ||<2, -1, 3>||1 = |2| + |-1| + |3| = 6.

Dustinsfl
How can I integrate cos(mx)*sin(nx) when they don't have the same angle?

Staff Emeritus
Homework Helper
Use a trig identity to rewrite the product of a sine and a cosine.

Dustinsfl
For the second problem, I don't know how to start the proof.

Mentor
Integration by parts twice would probably work, or you could look in a table of integrals. Since this isn't about learning to integrate, but is instead and application of integration, it seems reasonable to me to look it up in a table of integrals.

Dustinsfl
On the integration by parts comment, I have an unrelated issue. I was doing a Laplace Transform of e^(-st+t)*sin(t) but after doing integration by parts, I had a form of the original with a 1/(s-1) time the integral so I can't subtract across to the other side. What can I do there since if I keep going it will an endless cyclical cycle?

Dustinsfl
I have attached a update that show cos(mx) and sin(nx) are orthogonal; however, showing cos(mx) cos(mx) equals 1 isn't quite working.

#### Attachments

• Untitled (2).pdf
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Staff Emeritus