Use normal vectors to determine the intersection, if any, foreach of the following groups of three planes. Give a geometricinterpretation in each case and the number of solutions for thecorresponding linear system of equations. If the planes intersectin a line, determine a vector equation of the line. If the planesintersect in a point, determine the coordinates of the point.
a x + 2y + 3z = ?4
b x + 2y + 3z = ?4
2x + 4y + 6z = 7
2x + 4y + 6z = 7
x + 3y + 2z = ?3
3x + 6y + 9z = 5
c x + 2y + z = ?2
d x ? 2y ? 2z = 6 2x + 4y + 2z = 4 2x ? 5y + 3z = ?10 3x + 6y + 3z= ?6 3x ? 4y + z = ?1
e. x ? y + 3z = 4 x + y + 2z = 2 3x + y + 7z = 9
