Question

The resultant of two vectors acting at an angle 90 degree is √10.if two vectors acting at an angle 60 degree the resultant becomes√13 units. Find the values of the vectors​

Answer 1

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Given conditions,

Resultant (R) = √10 A

Magnitude of 2 vectors = 2A and √2 A

Using the Formula, for two vectors P and Q,

R² = P² + Q² + 2PQ Cosθ

⇒ 10A² = 4A² + 2A² + 2A × √2A Cosθ

⇒ 10A² = 6A² + 2√2 A Cosθ

∴ 2√2 A² Cosθ = 4A²

Cosθ = √2

Therefore, θ = Cos⁻¹(√2)

Hope it helps.

Answer 2

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Question:

The resultant of two vectors acting at an angle 90 degree is √10.if two vectors acting at an angle 60 degree the resultant becomes√13 units. Find the values of the vectors?

Answer:

Given conditions,

Resultant (R) = √10 A

Magnitude of 2 vectors = 2A and √2 A

Using the Formula, for two vectors P and Q,

R² = P² + Q² + 2PQ Cosθ

⇒ 10A² = 4A² + 2A² + 2A × √2A Cosθ

⇒ 10A² = 6A² + 2√2 A Cosθ

∴ 2√2 A² Cosθ = 4A²

Cosθ = √2

Therefore, θ = Cos⁻¹(√2)

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