Calculus Homework (Vectors)

[sllyanders87]

Hello everyone. I need help for question below

Find the equation of the plane through the point ?(?,?,−?) and perpendicular to the line of intersection of the planes ?? + ? − ? = ? and ? + ?? + ? = ?

 

[tkhunny]

Can you determine the line of intersection?

 

[sllyanders87]

Can you determine the line of intersection?

I only know by definition, first i should set the equations equal to each other and the solution will provide the intersection.

 

[tkhunny]

Let's see it. What is your result?

 

[sllyanders87]

Let's see it. What is your result?

n1=<2,1,-1>
n2=<1,2,1>
n1xn2= i(1+2)-j(2+1)+k(4-1)
n1xn2=<3,-3,3>
n3=<3,-3,3>
3(x-2)-3(y-1)+3(z-(-1))=0
3x-6-3y+3+3z+3=0
3x-3y+3z=0