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UPSC NDA I 2023 Mathematics Solved Paper

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Consider the following for the next two (02) items that follow :
Let
→
a
=3
^
i
+3
^
j
+3
^
k
 and
→
c
=
^
j
−
^
k
. Let
→
b
 be such that
→
a
⋅
→
b
=27 and
→
a
×
→
b
=
→
9c
[NDA I 2023]
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