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

MCQ

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

✓
$i$
B
$k$
C
$j$
D
$i + j + k$

✓

Answer

Correct option: A.

$i$

a
(a) Let $a = xi + yj + zk$.

Then $a\,.\,i = (xi + yj + zk)\,.\,i = x$ and $a\,.\,(i + j) = x + y$ and $a\,.\,(i + j + k) = x + y + z$

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 $x = 1$; $\therefore \,\,a = i$.

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