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National and Regional Contests
China Contests
(China) National High School Mathematics League
2023 China Second Round
4
A problem of Vectors
A problem of Vectors
Source: 2023 China Second Round Test 1 P4
June 2, 2024
vector
algebra
Problem Statement
if three non-zero vectors on a plane
a
⃗
,
b
⃗
,
c
⃗
\vec{a},\vec{b},\vec{c}
a
,
b
,
c
satisfy: (a)
a
⃗
⊥
b
⃗
\vec{a}\bot\vec{b}
a
⊥
b
(b)
b
⃗
⋅
c
⃗
=
2
∣
a
⃗
∣
\vec{b}\cdot\vec{c}=2|\vec{a}|
b
⋅
c
=
2∣
a
∣
(c)
c
⃗
⋅
a
⃗
=
3
∣
b
⃗
∣
\vec{c}\cdot\vec{a}=3|\vec{b}|
c
⋅
a
=
3∣
b
∣
find out the minimum of
∣
c
⃗
∣
|\vec{c}|
∣
c
∣
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