If r ,. ,i = r ,. ,j = r ,. ,k and |r| , , = 3, then r = - Vidyadip

MCQ

If $r\,.\,i = r\,.\,j = r\,.\,k$ and $|r|\,\, = 3,$ then $r = $

A
$ \pm \,3\,(i + j + k)$
B
$ \pm \,\frac{1}{3}\,(i + j + k)$
C
$ \pm \,\frac{1}{{\sqrt 3 }}\,(i + j + k)$
✓
$ \pm \,\sqrt 3 \,(i + j + k)$

✓

Answer

Correct option: D.

$ \pm \,\sqrt 3 \,(i + j + k)$

d
(d) Let $r = xi + yj + zk.$ Since $r.i = r.j = r.k$

$ \Rightarrow x = y = z$ .....$(i)$

Also $|r| = \sqrt {{x^2} + {y^2} + {z^2}} = 3 \Rightarrow x = \pm \sqrt 3 $, {By $(i)$}

Hence the required vector $r = \pm \sqrt 3 (i + j + k).$

Trick : As the vector $ \pm \sqrt 3 (i + j + k)$ satisfies both the conditions.

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