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

[RG11]

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


thanks!

 

[Squar3root]

I got (0, -1, 0) + λ(0, -6, 1) for a)

 

[RG11]

I got (0, -1, 0) + λ(0, -6, 1) for a)

could you go through how you got there?

 

[photastic]

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]

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

 

[InteGrand]

I got (0, -1, 0) + λ(0, -6, 1) for a)

That's a line lol.

 

[InteGrand]

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>.

 

[RG11]

thank you!