Let {\bo {a}}^{\to}=a_1 \stackrel{\^}{\bo {i}}+a_2 \stackrel{\^}{\bo {j}}+a_3 \stackrel{\^}{\bo {k}} Assertion (A) : The identity |{\bo {a}}^{\to} \times \stackrel{\^}{\bo {i}}|^2+|{\bo {a}}^{\to} \times \stackrel{\^}{\bo {j}}|^2+|{\bo {a}}^{\to} \times \stackrel{\^}{\bo {k}}|^2=2|{\bo {a}}^{\to}|^2 holds for {\bo{a}}^{\to}. Reason (R) : {\bo {a}}^{\to} \times \stackrel{\^}{\bo {i}}=a_3 \stackrel{\^}{\bo {j}}-a_2 \stackrel{\^}{\bo {k}}, {\bo {a}}^{\to} \times \stackrel{\^}{\bo {j}}=a_1 \stackrel{\^}{\bo {k}}-a_3 \stackrel{\^}{\bo {i}}, {\bo {a}}^{\to} \times \stackrel{\^}{\bo {k}}=a_2 \stackrel{\^}{\bo {i}}-a_1 \stackrel{\^}{\bo {j}} Which of the followingis correct ?

Correct Answer is : Both (A) and (R) are true and (R) is the correct reason for (A)

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

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

EAMCET Engineering 2007 Solved Paper

Section: Mathematics

Question : 119 of 160

Marks: +1, -0

Let

→

=a1

+a2

+a3

Assertion (A) : The identity
|

→

|2+|

→

|2+|

→

|2=2|

→

|2 holds for

→

.
Reason (R) :

→

=a3

−a2

→

=a1

−a3

→

=a2

−a1

Which of the followingis correct ?

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