# Homework Help: A vector question (Proof)

1. Oct 29, 2012

### ozon

Hello,
I am new at this forum. Firstly, I want to say I am happy to be a member of this forum. English is not my native language. So I can make some grammer and other mistakes. I try to write with no mistakes. If I make mistakes for writing, I apologize.
I have a question. You see a triangle in the picture. There are some vectors. h is height or short distance between p0 and V3. In the picture, you see an equation to find h. How do you prove this equation?

2. Oct 29, 2012

### Simon Bridge

Welcome to PF;
Have you tried starting with the definition of a vector cross-product?

3. Oct 30, 2012

### ozon

Thanks. Yes, I have. But I can't solve it.
h is norm of short distance between p0 and V3. So I have to use a new symbol for short distance. I want to call it as V4.
h=|V4|
|V4||V3|sin900=|V1xV2|
V4xV3=|V1xV2|
I have tried something but I have no idea. Some clues are very useful to prove this equation.

4. Oct 30, 2012

### Fightfish

HINT:
What does $h |V_{3}|$ give you?
What does $|V_{1} \times V_{2}|$ give you?
It is related to a property of the triangle.

5. Oct 30, 2012

### ozon

Thanks but I do not have any idea.

6. Oct 30, 2012

### Fightfish

Okay, I'll be a little more explicit: how would you go about finding the area of the triangle? There are two ways: 1st is by geometrical means, and 2nd by vectorial methods.

7. Oct 30, 2012

### ozon

Ok. First way is not problem to find area of the triangle. But I do not know how to find area of the triangle with vectorial methods. I think second way is necessary to prove this equation. Thanks for your clues. But I need more than them.

8. Oct 30, 2012

### Staff: Mentor

If A and B are the lengths of two sides of a triangle, and θ is the angle between the two sides, what is the equation for the area of the triangle in terms of A, B, and θ?

9. Oct 31, 2012

### ozon

Your clue is very helpful for me. Thanks. It is very easy now.
Area of triangle (1/2)h|V3|sin900=(1/2)|V1||V2|sinθ
h|V3|=|V1xV2|
h=(|V1xV2|)/|V3|
Thank you everybody for your helping.