Will medal and fan if you help me solve this beast

The plane through (1,2,−1) that is perpendicular to the line of intersection of the planes 2x+y+z=2 and x + 2y + z = 3.

Question

Will medal and fan if you help me solve this beast

The plane through (1,2,−1) that is perpendicular to the line of intersection of the planes 2x+y+z=2 and x + 2y + z = 3.

irishboy123 · Answer

looks fine

christos · Answer

? Do you know how to solve it ? @IrishBoy123  I am not sure what you mean by "it looks fine"

irishboy123 · Answer

what i mean is that i did what the did and got the same answers.  do you get something different?

mathmate · Answer

|dw:1477997950861:dw|

christos · Answer

@IrishBoy123 If you are refering to the previews question I posted.... I think he replaced x rong... because he sets x to 1.... but x vanishes completely ... that's for the previews question...

christos · Answer

sets x to 0 ... x vanishes ... sets x to 1 .... x vanishes again ...

irishboy123 · Answer

nah, look how the -2 becomes a 2 

it's done in one step

reemii · Answer

It's a two step solution.
1. compute the vector $\vec v_3 = \vec v_1  \times\vec  v_2 = (a,b,c)$  as @mathmate illustrated -> this is the normal vector of the plane to find
2. use the fact that $(1,2,-1)$ belongs to the plane to find the $d$ in the equation 
          $$ax+by+cz+d=0.$$

reemii · Answer

Do you find $\vec v_3 = (-1,-1,3)$ ?

reemii · Answer

@Christos