Parameterize the plane through the point (−1,−3,1) with the normal vector ⟨−4,4,3⟩ r⃗ (s,t)= (Use s and t for the parameters in your parameterization, and enter your vector as a single vector, with angle brackets: e.g., as .)

Question

Parameterize the plane through the point (−1,−3,1) with the normal vector ⟨−4,4,3⟩
r⃗ (s,t)=  
(Use s and t for the parameters in your parameterization, and enter your vector as a single vector, with angle brackets: e.g., as < 1 + s + t, s - t, 3 - t >.)

anonymous · Answer

i did (-4)(s+1)+4(t+3)3(z-1)=0

anonymous · Answer

simplifying to <4/3x, -4/3t,-5/3> but that's not right.  what'd i do wrong?

ganeshie8 · Answer

try
<-1+s, -3+s-3t, 1+4t>

anonymous · Answer

ok yeah.  how'd you do that?

ganeshie8 · Answer

you just need to find two vectors perpendicular to the given normal vector

ganeshie8 · Answer

normal vector : <-4, 4, 3> you can guess them, clearly <1, 1, 0> is perpendicular to the normal vector because the dot product will be 0, yes ?

anonymous · Answer

yes

ganeshie8 · Answer

find another  vector perpendicular to the normal vector

anonymous · Answer

<1,1,0> is perpendicular, why would i need to find another one?  i'm confused.

ganeshie8 · Answer

suppose you're in xy plane

ganeshie8 · Answer

how many vectors do you need to fill the entire plane ?

ganeshie8 · Answer

I give you the vector <1, 0>
can you fill the entire plane by adding this vector as many times as you want ?

ganeshie8 · Answer

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ganeshie8 · Answer

if you add it two times you reach the point  (1, 0) + (1, 0) = (2, 0)

if you subtract it two times you reach the point (-2, 0)

ganeshie8 · Answer

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