Write a vector equation of the line that passes through p(4,7) and is parallel to a=(3,8)

L: ( 4 , 7 ) + t*( 3 , 8 )

Step-by-step explanation:

Solution:-

- The vector equation of line is represented by the following form:

                 L: ( xo , yo ) + t * ( dx , dy )

Where,

- ( xo , yo ) : The position coordinates of any point that lies on the line

- t : A parameter that defines unit distance between an arbitrary point on the line and the fixed point ( xo , yo ).

-  ( dx , dy ): The direction vector of the line representing the slope/direction/orientation of the line in the coordinate system.

- We are given a point through which the line passes as p ( 4 , 7 ) and the line " L" is parallel to the direction vector a = ( 3 , 8 ).

- The direction vectors of all parallel lines have the same orientation. So the direction of vector is similar to that of a = ( 3 , 8 ).

- Therefore we write our vector equation of the line as follows:

                L: ( 4 , 7 ) + t*( 3 , 8 )

- We can express the vector equation of line in parametric form as follows:

               x1 = 4 +3t

               y1 = 7 + 8t

Where,

            ( x1 , y1 ) are the position coordinates of any arbitrary point on line. "L"