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sepia

Novice

Registered: 2024-01-15

Posts: 2

Area under tangent using vectors

A circle with a radius of 10 has its center at (25, 0). There is a line/ray from the origin that touches the circle at one place. What is the area under the line from the origin up to the point?

I have come up with a solution using a line equation and the discriminant but I would like to solve it with vectors. I can only see that a dot product results in zero and that's as far as I can get.

Thanks.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,640

Re: Area under tangent using vectors

hi sepia

Welcome to the forum.

You need the cross product (vector product). The formula is

https://www.mathsisfun.com/algebra/vect … oduct.html

In effect it's the formula

where theta is the angle betwen the sides a and b.

You will still have to find the coordinates of the point where the tangent intersects the circle.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

sepia

Novice

Registered: 2024-01-15

Posts: 2

Re: Area under tangent using vectors

Thanks Bob.

Does the cross product work for 2D?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,640

Re: Area under tangent using vectors

Yes. The 'theory' states that the area is a vector at right angles to the two lines, which might seem a bit odd but the magnitude is correct.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob