For any three vectors A, B & C. If Ā= B - C, determine the angle between A & B and B & C.
Answers
Answered by
1
Step 1: Squaring the given equation and simplifying it
Let θ be the angle between
a
and
b
.
Given:
a
+
b
=
c
Squaring on both sides :
a
+
b
)⋅(
a
+
b
)=
c
⋅
c
⇒ ∣
a
∣
2
+∣
b
∣
2
+2(
a
⋅
b
)=∣
c
∣
2
⇒ ∣
a
∣
2
+∣
b
∣
2
+2∣
a
∣∣
b
∣cosθ=∣
c
∣
2
....(1) [∵
a
⋅
b
=∣
a
∣∣
b
∣cosθ]
We are also given;
∣
a
+∣
b
∣=∣
c
∣
Squaring above equation
⇒∣
a
∣
2
+∣
b
∣
2
+2∣
a
∣∣
b
∣=∣
c
∣
2
....(2)
Step 2: Comparing the equations
Comparing eq
n
(1) and (2)
We get, cosθ=1
⇒
θ=0
∘
Hence option C is correct.
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