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Question : 111 of 180
Marks:
+1,
-0
Solution:
To solve for
||, we use the given equation:
|×|2+|⋅|2=144and the given magnitude
||=4.
Recall the identities of the dot product and cross product for vectors
and
:
The magnitude of the dot product is given by:
|⋅|=||||cos‌θ The magnitude of the cross product is given by:
|×|=||||sin‌θSubstitute these identities into the given equation:
‌(||||sin‌θ)2+(||||cos‌θ)2=144‌(4||sin‌θ)2+(4||cos‌θ)2=144Factor out
|| :
16||2(sin‌2θ+cos2θ)=144Since
sin‌2θ+cos2θ=1, we have:
16||2=144 Solve for
||2 :
‌||2=‌‌||2=9Take the square root of both sides:
||=3.Therefore, the correct option is:
Option A = 3
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