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# Let $\overrightarrow {a}=a_1\hat i+a_2 \hat j+a_3 \hat k$ Assertion (A): The identify $|\overrightarrow a \times \hat i |^2+|\overrightarrow a \times \hat j|^2+|\overrightarrow a \times \hat k| ^2=2 | \overrightarrow a |^2$ holds for $\overrightarrow {a}$. Reason (R): $\overrightarrow {a} \times \hat i =a_3 \hat j- a_2 \hat k, \overrightarrow a \times \hat j= a_1 \hat k- a_3 \hat i, \overrightarrow a \times \hat k=a_2 \hat i- a_1 \hat j$ Which of the following is correct ?

(a) Both (A) and (R) are true and (R) is the correct reason for (A)

(b) Both (A) and (R) are true but (R) is not the correct reason for (A)

(c) (A) is true, (R) is false

(d) (A) is false, (R) is true

Can you answer this question?

## 1 Answer

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(a) Both (A) and (R) are true and (R) is the correct reason for (A)
answered Nov 7, 2013 by

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