Calc III problem:
Find an equation of the plane that contains the y-axis and makes an angle of (pi/6) with the positive x-axis.

I'm a little stuck. So far I understand that since the point contains the y-axis, then the plane should contain (0,0,0). After that, I'm sort of stuck. Thank you

Question

Calc III problem:
Find an equation of the plane that contains the y-axis and makes an angle of (pi/6) with the positive x-axis.

I'm a little stuck. So far I understand that since the point contains the y-axis, then the plane should contain (0,0,0). After that, I'm sort of stuck. Thank you

ganeshie8 · Answer

start by finding the normal vector of plane

ganeshie8 · Answer

since the plane contains y axis, the y component of normal vector must be 0

anonymous · Answer

So the normal vector is (pi/6, 0, c)?

ganeshie8 · Answer

Also since the angle between normal vector and x axis is pi/6, the x component is same as the direction cosine :  cos(pi/6) = sqrt(3)/2

anonymous · Answer

OHH the y component

ganeshie8 · Answer

the unit normal vector will be :  $\langle \frac{\sqrt{3}}{2}, 0, c \rangle$

ganeshie8 · Answer

you can find the z component by setting the magnitude equal to 1

ganeshie8 · Answer

$\large  (\frac{\sqrt{3}}{2})^2 + 0^2 + c^2 = 1$

solve $c$

anonymous · Answer

And then you can use (0,0,0) as your point to solve for the equation of plane right?

ganeshie8 · Answer

Oh yes !

ganeshie8 · Answer

equation of plane with normal vector <a,b,c> is
ax + by + cz = p

anonymous · Answer

Oh.. will it still work if I plug into the scalar equation form?

anonymous · Answer

like a(x-xnot) etc etc

ganeshie8 · Answer

it will work

anonymous · Answer

So should I get (sqrt(3)/2)x +0.5z = 0    ?

ganeshie8 · Answer

looks perfect ! u may multiply by 2 if  want

anonymous · Answer

Thank you so much!

ganeshie8 · Answer

yw!