Question

If $a.i = a.(i + j) = a.(i + j + k)$, then a =

• A. i
• B. k
• C. j
• D. i + j + k

Answer 1

Answer: (A)

i

Answer 2

Let $\mathbf{a} = x\mathbf{i} + y\mathbf{j} + z\mathbf{k}$.

Then $\mathbf{a}.\mathbf{i} = (x\mathbf{i} + y\mathbf{j} + z\mathbf{k}).\mathbf{i} = x$ and $\mathbf{a}.(\mathbf{i} + \mathbf{j}) = x + y$ and

$\mathbf{a}.(\mathbf{i} + \mathbf{j} + \mathbf{k}) = x + y + z$

$\because$ Given that $x = x + y = x + y + z$

Now$x = x + y \Rightarrow y = 0$and $x + y = x + y + z \Rightarrow z = 0$

Hence $x = 1$; $\therefore\mathbf{a} = \mathbf{i}$.