The value of hat{ i } times(hat{ i } times a | vedclass

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Question

(c)
Suppose $a =a_1 \hat{ i }+a_2 \hat{ j }+a_3 \hat{ k }$
Now, $\quad(\hat{ i } 	imes a )=a_2 \hat{ k }-a_3 \hat{ j }$
Now, $\quad \hat{ i } 	im

Vedclass · Accepted Answer

$-2\,a$

Vedclass · Answer

(c)
Suppose $a =a_1 \hat{ i }+a_2 \hat{ j }+a_3 \hat{ k }$
Now, $\quad(\hat{ i } 	imes a )=a_2 \hat{ k }-a_3 \hat{ j }$
Now, $\quad \hat{ i } 	imes(\hat{ i } 	imes a )=-a_2 \hat{ j }-a_3 \hat{ k }$
Similarly, $\quad \hat{ j } 	imes(\hat{ j } 	imes a )=-a_1 \hat{ i }-a_3 \hat{ k }$
and $\quad \hat{ k } 	imes(\hat{ j } 	imes a )=-a_1 \hat{ i }-a_2 \hat{ j }$
$	herefore \quad \hat{ i }(\hat{ i } 	imes a )+\hat{ j }(\hat{ j } 	imes a )+\hat{ k }(\hat{ k } 	imes a )=-2 a$

The value of $\hat{ i } \times(\hat{ i } \times a )+\hat{ j } \times(\hat{ j } \times a )+\hat{ k } \times(\hat{ k } \times a )$ is

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