If a + b + c = 0, and |a| = 3, |b| = 5, |c| = 7, then what is the angle between a and b?

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Navik GD 2022 (All Shift) Memory Based Paper (Section I + II)

Answer 1

Concept:

If θ is the angle between x and y then x.y = xycosθ

Calculation:

GIven, a + b + c = 0

⇒ a + b = -c, squaring both sides we get

⇒ (a + b)² = (-c)²

⇒ |a + b|2 = |c|2

⇒ |a|² + |b|² +2|a||b|cosθ = |c|², where θ = angle betwee a and b

Putting the values we get,

3²+ 5² + 2× 3× 5 cosθ = 7²

⇒ 9 + 25 + 30cosθ = 49

⇒ 30cosθ = 49 - 34 = 15

⇒ cosθ = \(1\over 2\)

∴ θ = 60°

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