SOLUTION: Find the equation of the line joining (1,3,-1) to (2,4,7). Show that it is parallel to the plane 2x+6y-z=5

Instead of doing your problem for you, I will instead do one exactly like
yours step by step so you can use it as a model to do yours by:

A parametric equation for a line through the point



parallel to the vector



is:



A symmetric equation for the line is



-----------------------------

To find a vector parallel to the line, 



we subtract coordinates:



A parametric equation for the line is then:





A symmetric equation for the line is







--------------------

Given the equation of the plane  x-2y+z=7, a normal to the plane is
a vector whose components are the coefficients of x,y and z in the
equation of the plane.  So

  is a vector normal to the plane 
x+2y-z=7.

So we merely have to show that  is
perpendicular to the vector parallel to the line, which is    

To show two vectors are perpendicular we show that their dot product is 0.

•.

Now do yours exactly the same way.

Edwin