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Find the magnitude of the sum of a 10m displacement and a 5 -m displacement when the angle between them is 45

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Onyebuchinnajiidn

Answer:

The magnitude of the resultant of the two vectors is 7.37 m.

Explanation:

let the first vector = a = 10 m

let the second vector = b = 5 m

angle between the two vectors, θ = 45⁰

The magnitude of the resultant of the two vectors is calculated as;

[tex]R^2 = a^2 + b^2 -2ab \times cos(\theta)\\\\R^2 = 10^2 + 5^2 - [2\times 10 \times 5 \times cos(45)]\\\\R^2 = 125 - [100 \times 0.7071]\\\\R^2 = 125 -70.71\\\\R^2 = 54.29 \\\\R= \sqrt{54.29} \\\\R = 7.37 \ m[/tex]

Therefore, the magnitude of the resultant of the two vectors is 7.37 m.

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