desperate for help for the ONE question (HAVE class test tommorow) (1 Viewer)

RG11

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Find the parametric vector forms to describe the following planes in R^3.
a) x2+6x3 = -1
b) x3=2


thanks!
 

photastic

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Find the parametric vector forms to describe the following planes in R^3.
a) x2+6x3 = -1
b) x3=2


thanks!
a) above reply.
b) x = (0,0,2) + λ1(1,0,0) + λ2(0,1,0) where λ1,λ2 are R
 

InteGrand

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Find the parametric vector forms to describe the following planes in R^3.
a) x2+6x3 = -1
b) x3=2


thanks!
For b), it's just (i.e. like the x-y plane, but shift it up by two units, since that's what the equation is geometrically).

Edit: just got answered
 
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InteGrand

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Find the parametric vector forms to describe the following planes in R^3.
a) x2+6x3 = -1
b) x3=2


thanks!
For a), since x1 does not appear in the equation, we can set it equal to a free parameter λ ∈ ℝ. Also, set x3 = μ ∈ ℝ. Then the plane's equation implies that x2 = -6x3 – 1 = -6μ – 1.

Then x = <x1,x2,x3>
= <λ,-6μ – 1,μ>

= <0,-1,0> + λ<1,0,0> + μ<0,-6,1>.
 

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