Find b and c so that (7, b,

c. is orthogonal to both (1, 2, 3) and (1, - 2, 1).

The cross product is perfect for this purpose.

The cross product C of vectors p and q is orthogonal to both p and q.

C will then be scaled to have the first value equal to 7 to find b and c.

C=x

=

i j k

1 2 3

1 - 2 1

=

=

=2

= (8/7)

= (8/7)

So b=7/4, c=-7/5

Check:

. = 7*1+7/4*2-7/5*3=7+7/2-21/2=0 ... ok, orthogonal

.=7*1-7/4*2-7/2*1=0 ... ok, orthogonal