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Joint Entrance Examination
Mathematics
Vector Algebra
Question 164
Question 164 of 379
Easy
NUMERICAL
Let
a
⃗
,
b
⃗
\vec a,\vec b
a
,
b
be vectors with
∣
a
⃗
∣
=
14
|\vec a|=\sqrt{14}
∣
a
∣
=
14
,
∣
b
⃗
∣
=
6
|\vec b|=\sqrt{6}
∣
b
∣
=
6
,
∣
a
⃗
×
b
⃗
∣
=
48
|\vec a\times\vec b|=\sqrt{48}
∣
a
×
b
∣
=
48
. Then
(
a
⃗
⋅
b
⃗
)
2
(\vec a\cdot\vec b)^2
(
a
⋅
b
)
2
is equal to \_\_\_\_\_\_\_. Answer: 36
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Official solution
\[|\vec a\times\vec b|^2+(\vec a\cdot\vec b)^2 = |\vec a|^2|\vec b|^2 \implies 48+(\vec a\cdot\vec b)^2 = 14\times6=84 \implies (\vec a\cdot\vec b)^2=36\]
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