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Answer 1

Answer:

60°

Step-by-step explanation:

Given, |a| = 3, |b| = 5, |c| = 7.

Given, a + b + c = 0

⇒ |a + b| = |-c|.

On squaring both sides, we get

⇒ |a + b|² = |-c|²

⇒ |a|² + |b|² + 2|a||b|cosθ = |c|²

⇒ 9 + 25 + 2 * 3 * 5 * cosθ = 49

⇒ 34 + 30 cosθ = 49

⇒ 30 cos θ = 15

⇒ cos θ = 15/30

⇒ cos θ = 1/2

⇒ cos θ = cos 60°

⇒ θ = 60°.

Therefore, the angle between a and b = 60°.

Hope it helps!

Answer 2

Answer:

60°

Step-by-step explanation:

|a| = 3, |b| = 5, |c| = 7.

a + b + c = 0

|a + b| = |-c|.

On squaring both sides, we get

|a + b|² = |-c|²

|a|² + |b|² + 2|a||b|cosθ = |c|²

9 + 25 + 2 * 3 * 5 * cosθ = 49

34 + 30 cosθ = 49

30 cos θ = 15

cos θ = 15/30

cos θ = 1/2

cos θ = cos 60°

θ = 60°.

the angle between a and b = 60°.