Another approach to ﬁnding the line of intersection of the two planes

x+6y+z=4 0 4 0

x: 1 +1» —2 +,u —3

0 0 4 is to ﬁrst convert both into Cartesian form, and then solve the system of two equations. Since a normal vector to the second equation is n = ‘ <-8,-16,-12> 9|. '3 and the oo-ordinate vector for a point on the plane is p = we can write the second plane in point-normal form: and <o,1,0> all; B (x — p) - n = 0.

Note: the Maple syntax for a vector is <1 , 2 , 3). This becomes the Cartesian equation 2*x+4“y+3‘z=4 o I. . Note: the maple syntax for the Cartesian equation x + 6 y + z = 4 is x + 6 * y + z = 4. 1 6 1

Reducing the system of two linear Cartesian equations to row—echelon form leads us to the augmented matrix (A | b) whereA = ( ) and b = Note: enter 1] as a two dimensional vector, e.g. <1 , 2>. From this we can determine that the intersection of the two planes is a line which is parallel to the vector I3 and where g is the oo-ordinate vector for a point on the line. <8,0,-4> 9' Note: use the Maple syntax for a vector for both these answers, e.g. <1 , 2 , 3>.