Question

A vector $a$ can be written as

• A. $(a\cdot i)i+(a\cdot j)j+(a\cdot k)k$
• B. $(a\cdot j)i+(a\cdot k)j+(a\cdot i)k$
• C. $(a\cdot k)j+(a\cdot i)j+(a\cdot j)k$
• D. $(a\cdot a)i+(i+j+k)k$

Answer 1

The correct option is A $(a\cdot i)i+(a\cdot j)j+(a\cdot k)k$

Let $a=a_{1}i+a_{2}i+a_{3}k$, so that $a.i=a_1,a\cdot j=a_2$ and $a.k=a_3$
$\Rightarrow a=(a\cdot i)i+(a\cdot j)j+(a\cdot k)k$