Question

$(a.i)i+(a.j)j+(a.k)k$ is equal to?

• A. $a$
• B. $2a$
• C. $3a$
• D. $0$

Answer 1

The correct option is A

$a$

Finding the value of :

Consider, $a=xi+yj+zk$ where, $i,j,k$are the unit vectors in ‘x’, ‘y’ & ‘z’ direction respectively.

Now,

$\begin{array}{rcl}& & (a.i)i+(a.j)j+(a.k)k\\ & =& \left[\right(xi+yj+zk).i]i+\left[\right(xi+yj+zk).j]j+\left[\right(xi+yj+zk).k]k\\ & =& xi+yj+zk\mathbf{}\mathbf{[}\mathbf{\because }\mathit{i}\mathbf{.}\mathit{j}\mathbf{=}\mathit{j}\mathbf{.}\mathit{k}\mathbf{=}\mathit{k}\mathbf{.}\mathit{i}\mathbf{=}\mathbf{0}\mathbf{]}\\ & =& a\end{array}$

Hence, correct option is $\mathbf{\left(}\mathit{A}\mathbf{\right)}\mathbf{.}$