3. The magnitude of vectors A, B and C are 3, 4 and 5 units respectively. If Ä+B = 7, then the angle between A and B is
Answers
Answer:
Squaring the given equation on both sides
Let θ be the angle between
A
and
B
A
+
B
=
C
Squaring on both sides
(
A
+
B
)
2
=(
C
)
2
⇒∣
A
∣
2
+∣
B
∣
2
+2
A
.
B
=∣
C
∣
2
⇒∣
A
∣
2
+∣
B
∣
2
+2∣
A
∣∣
B
∣cosθ=∣
C
∣
2
....(1)
Step 2: Calculations
Put the values of all the variables in eq (1) to get θ
(3)
2
+(4)
2
+2×3×4cosθ=(5)
2
⇒ cosθ=0
⇒ θ=90
∘
Step-by-step explanation:
Squaring the given equation on both sides
Let θ be the angle between
A and B
A + B = C
Squaring on both sides
( A + B ) ^2 =( C ) ^2
⇒∣ A ∣ ^2 +∣ B ∣^ 2 +2 A . B =∣ C ∣ ^2
⇒∣ A ∣^ 2 + ∣ B ∣^ 2 +2 ∣A∣∣B∣ cos θ=∣ C ∣ ^2
....(1)
Step 2: Calculations
Put the values of all the variables in eq (1) to get θ
(3) ^2 +(4)^2+2×3×4cosθ=(5) ^2
⇒ cosθ=0
⇒ θ=90∘