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# Another approach to nding 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 rst convert both into Cartesian form,...

hi, i have no idea to solve this question.

I try to do that. but it is still not correct...

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 = ‘ &lt;-8,-16,-12&gt; 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 &lt;o,1,0&gt; all; B (x — p) - n = 0.
Note: the Maple syntax for a vector is &lt;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. &lt;1 , 2&gt;. 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. &lt;8,0,-4&gt; 9' Note: use the Maple syntax for a vector for both these answers, e.g. &lt;1 , 2 , 3&gt;.

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