Mathematics

Problem

Let

\mathbf a = 3\hat i - \hat j + 4\hat k

and

\mathbf b = 2\hat i + 2\hat j - 2\hat k

. (a) Show that

\mathbf a

and

\mathbf b

are not parallel. (b) Find a vector

\mathbf r

that is perpendicular to both

\mathbf a

and

\mathbf b

and whose magnitude is

5

. (c) Verify that your vector

\mathbf r

is indeed perpendicular to

\mathbf a

and

\mathbf b

. (d) Determine all unit vectors that are perpendicular to both

\mathbf a

and

\mathbf b