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If and are unit vectors satisfying
MATHEMATICS · Subjective · A Level · Mathematics · Vectors · Vectors
Problem
If
a
⃗
,
b
⃗
\vec{a}, \vec{b}
a
,
b
and
c
⃗
\vec{c}
c
are unit vectors satisfying
∣
a
⃗
−
b
⃗
∣
2
+
∣
b
⃗
−
c
⃗
∣
2
+
∣
c
⃗
−
a
⃗
∣
2
=
9
|\vec{a} - \vec{b}|^2 + |\vec{b} - \vec{c}|^2 + |\vec{c} - \vec{a}|^2 = 9
∣
a
−
b
∣
2
+
∣
b
−
c
∣
2
+
∣
c
−
a
∣
2
=
9
, then
∣
2
a
⃗
+
5
b
⃗
+
5
c
⃗
∣
|2\vec{a} + 5\vec{b} + 5\vec{c}|
∣2
a
+
5
b
+
5
c
∣
is equal to
Related theory
Vector Operations
Vectors
Dot Product
Scalar product
Vector Algebra
Dot product of two vectors
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