+0  
 
0
193
2
avatar

Let P be the plane \(x + y + z = 0. \)
a) Find a vector lying in the plane.
b) Find a vector that is orthogonal to the plane (normal)

 

Thanks in advance!

 May 12, 2019
 #1
avatar+106533 
+1

We have that 

x + y + z  = 0

 

We need two vectors in the plane to find an orthogonal vector 

 

The points    (1, 1, - 2) , (0, 1, -1)  and (6,-6, 0)   will lie in the plane

One vector lyimg in the plane will be  ( 0-1, 1 -1 , -1 - -2)  =  (-1, 0, 1) = -1i + 0j + 1k

Another will be  ( 6 - 1, -6,-1, 0 - -2)  = ( 5, -7, 2)  = 5i - 7j + 2k

 

We can use the cross-prduct to find a vector normal to the plane

 

i       j      k       i       j

-1    0     1      -1      0

5    -7     2       5     -7

 

[ (0*2)i + (1*5)j + (-1*-7)k ] - [(5*0)k + (-7*i)i + (2*-1)j ]  =  7i  + 7j + 7k

 

 

cool cool cool 

 May 12, 2019

33 Online Users

avatar
avatar
avatar
avatar
avatar
avatar
avatar