If a is any vector in space, then - Vidyadip

MCQ

If $ a$ is any vector in space, then

✓
$a = (a\,.\,i)\,i + \,(a\,.\,j)\,j + \,(a\,.\,k)\,k$
B
$a = (a\, \times \,i) + \,(a\, \times \,j)\, + \,(a\, \times \,k)\,$
C
$a = j\,(a\,.\,i)\, + k\,(a\,.\,j)\, + \,i\,(a\,.\,k)\,$
D
$a = (a\, \times \,i) \times i + \,(a\, \times \,j) \times j\, + \,(a\, \times \,k) \times k\,$

✓

Answer

Correct option: A.

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

a
(a) Let$a = {a_1}i + {a_2}j + {a_3}k,$then $a.i = {a_1},$ $a.j = {a_2},$ $a.k = {a_3}$

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

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