We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website. cookie policy and privacy policy.
 
+0  
 
0
103
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+102417 
+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

7 Online Users