Question

how to find a vector x perpendicular to u and v. Where u = [3,-7,4] and v = [-1,2,-2]

Answer 1

Let vector x = c [1, a, b ] 

Dot product of perpendicular vectors is 0.

c (3 - 7a + 4b ) = 0     => 7a - 4b = 3
c (-1 + 2a -2b ) = 0    =>  2a - 2b = 1

solving ,    a = 1/3    b = -1/6

x = c [ 1, 1/3, -1/6 ]   where c is any real number