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JEE Advanced 2018 Paper 1 Mathematics Q12
Mathematics
Problem
Let
a
⃗
\vec{a}
a
and
b
⃗
\vec{b}
b
be two unit vectors such that
a
⃗
\vec{a}
a
·
b
⃗
\vec{b}
b
= 0. For some x, y ∈ ℝ, let
c
⃗
\vec{c}
c
= x
a
⃗
\vec{a}
a
+ y
b
⃗
\vec{b}
b
+ (
a
⃗
\vec{a}
a
×
b
⃗
\vec{b}
b
). If |
c
⃗
\vec{c}
c
| = 2 and the vector
c
⃗
\vec{c}
c
is inclined at the same angle α to both
a
⃗
\vec{a}
a
and
b
⃗
\vec{b}
b
, then the value of 8 cos²α is _____.
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