If a=i+3j+k and b=i+12j+k, find a unit vector with positive first coordinate orthogonal to both a and

b.

The cross product of the vectors will be orthogonal to both:

axb

[tex]=x

=

i j k

1 3 1

1 12 1

=

=

Since it is required to have positive first coordinate, we reverse the sign of the components, namely reverse the direction of the vector, which is still orthogonal to both a and b:

Required vector is which is orthogonal to both a and b.