Find a nonzero vector x perpendicular to the vectors v 2 7

Find a non-zero vector x perpendicular to the vectors v = [2 -7 3] and u = [-1 4 2] x = [-1 -7 -26].

Solution

Let,

x=(a,b,c)

x.v=0, x.w=0

2a-7b+3c=0

-a+4b+2c=0

Adding twice of second equation to first one gives

b+7c=0 ie    b=-7c

-a+4b+2c=0 ie -a+4*(-7c)+2c=0

-a-26c=0

a=-26c

So,

x=(-26c,-7c,c)

Set, c=1

x=(-26,-7,1)