Question

Find the normal vector n to the plane, containing vectors: A = 3i +j - k and B = -i +k.

Answer 1

let direction ratio of normal vector is a , b , and c
n^ = a i +b j + c k
given ,
A =(3 i + j - k )
B =( - i + k )

because n^ vector perpendicular to both A and B

so,
A.n =0 =3a + b -c --------(1)

B.n = 0 = -a + c =0

-a + 0.b +c =0 ---------(2)

use Cramer rule ,

a/(1 -0) = -b/(3 - 1) = c/(0 + 1)

a/ 1 = b/-2 = c/1

hence,
a=1
b= -2
c=1

so, normal vector n^ = i - 2 j + k