Let , a, b and c be the length of three sides of triangle, represented in terms of vectors as .
Now, vector of same Magnitude acts as normal vector to each side.
So, equation of any vector p having normal q is given by
Now sum of three vector and it's normal is given as
Cross product of two identical vectors is Zero.
Given:
The equation of a circle is
A tangent line l to the circle touches the circle at point P(1,3).
To find:
The equation of the line l.
Solution:
Slope formula: If a line passes through two points, then the slope of the line is
Endpoints of the radius are O(0,0) and P(1,3). So, the slope of radius is
We know that the radius of a circle is always perpendicular to the tangent at the point of tangency.
Product of slopes of two perpendicular lines is always -1.
Let the slope of tangent line l is m. Then, the product of slopes of line l and radius is -1.
The slope of line l is and it passs through the point P(1,3). So, the equation of line l is
Adding 3 on both sides, we get
Therefore, the equation of line l is .