Equations of Lines

[K_Swiss]

Determine the parametric equations of each of the following planes:

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g) the plane containing the 2 intersecting lines:

r = (5,4,2) + t(4,-2,1)
r = (1,6,-6) + s(6,-4,4)


My Attempt:
x = 5 + 4t + 6s
y = 4 -2t - 4s
z = 2 + t + 4s

####What did I do wrong in this question? Please point out and correct my mistake!

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h)the plane containing the point (8,3,5) and the line:

r = (1,3,-1) + t(2,2,-5)


My Attempt:
x = 8 + 2t
y = 3 + 2t
z = 5 - 5t

####How do I find the other direction vector for this question?

 

[pka]

For part g. The two lines do not intersect.
Check the wording.

For part h. If \(\displaystyle N = \left\langle {7,0,6} \right\rangle \times \left\langle {2,2, - 5} \right\rangle \,\& \,P8,3,5)\) use the vector N as the normal to write the plane containing the point P.