If ⃗ a+ ⃗⃗ b+ ⃗c= ⃗ ⃗ , | ⃗ a| = 3, | ⃗⃗b| = 5 and | ⃗⃗⃗f| = 7 find a+b ⃗ . ⃗⃗b+c ⃗⃗ .c+a ⃗
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Answer:
We have ∣
a
∣=1,∣
b
∣=1,∣
c
∣=1
Also
a
+
b
+
c
=
0
Squaring we get,
∣
a
∣
2
+∣
b
∣
2
+∣
c
∣
2
+2(
a
⋅
b
+
b
⋅
c
+
c
⋅
a
)=0
⇒1+1+1+2(
a
⋅
b
+
b
⋅
c
+
c
⋅
a
)=0
∴
a
⋅
b
+
b
⋅
c
+
c
⋅
a
=−
2
3
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