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JEE Advanced 2019 Paper 2 Mathematics Q14
Mathematics
Problem
Let
a
⃗
\vec{a}
a
= 2î + ĵ −
k
^
\hat{k}
k
^
and
b
⃗
\vec{b}
b
= î + 2ĵ +
k
^
\hat{k}
k
^
be two vectors. Consider a vector
c
⃗
\vec{c}
c
= α
a
⃗
\vec{a}
a
+ β
b
⃗
\vec{b}
b
, α, β ∈ ℝ. If the projection of
c
⃗
\vec{c}
c
on the vector (
a
⃗
\vec{a}
a
+
b
⃗
\vec{b}
b
) is 3√2, then the minimum value of (
c
⃗
\vec{c}
c
− (
a
⃗
\vec{a}
a
×
b
⃗
\vec{b}
b
)) ·
c
⃗
\vec{c}
c
equals _____.
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