Answer to Question #60947 in Analytic Geometry for Subhay nazir

Question

Vectors intersection question:
A line can either lie on a plane, lie parallel to it or intersect it.
Determine, if there is one, the point of intersection between the line given by the equation:
x-5/2= y-1/-1 = z-15/4 and the plane given by the equation:
[x,y,z]= [-2,-7,5]+ s[2,6,3]+ t[1,4,-1]

b)Determine the angle between the line and the plane.
c)Give the equation of a plane and three lines, one of which is parallel to the plane, one of which lies on the plane, and one of which intersects the plane.