Question

If a is any vector in space, then show that a=(a.I)i+(a.J)j+(a.K)k

Answer 1

Answer:

Let a=xi+yj+zk

Now, (a.i)i+(a.j)j+(a.k)k=[(xi+yj+zk).i]i+[(xi+yj+zk).j]j+[(xi+yj+zk).k]k

=xi+yj+zk=a