sarah A

The perimeter of a triangle, its area, and the radius of the circle inscribed in the triangle are related in an interesting way. Prove that the radius of the circle times the perimeter of the triangle equals twice the area of the triangle.

Given a vector u, the familiar absolute-value notation |u| is often used for its magnitude. Thus the expressions u•u and |u|2 both mean the same thing. What exactly do they mean?

For any two numbers a and b, the product of a−b times itself is equal to a2−2ab+b2. Does this familiar algebraic result hold for dot products of a vector u − v with itself? In other words, is it true that (u − v) • (u − v) = u•u−2u•v+v•v? Justify your con...

Let u = [2,−3, 1] and v = [0, 1, 4]. Calculate the vector u − v. Place u and v tail-to-tail to form two sides of a triangle. With regard to this triangle, what does u−v represent? Calculate the number u•u and discuss its relevance to the diagram you have...

Let u = [2,−3, 1] and v = [0, 1, 4]. Calculate the vector u − v. Place u and v tail-to-tail to form two sides of a triangle. With regard to this triangle, what does u−v represent? Calculate the number u•u and discuss its relevance to the diagram you have...