Dois vetores são dados por ~a = (4,0 m)̂i− (3,0 m)ĵ + (1,0 m)k̂ ~b = (−1,0 m)̂i+ (1,0 m)ĵ + (4,0 m)k̂ Determine, em termos de vetores unitários, ...

Dois vetores são dados por ~a = (4,0 m)̂i− (3,0 m)ĵ + (1,0 m)k̂ ~b = (−1,0 m)̂i+ (1,0 m)ĵ + (4,0 m)k̂ Determine, em termos de vetores unitários, (a) (a) ~a+~b; (b) ~a−~b; (c) um terceiro vetor, ~c, tal que ~a−~b+~c = 0.

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Desenvolvendo com Questões

14/04/2024

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Física • Faculdade ChristusFaculdade Christus

Raul Capelo

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Ed

14.04.2024

Para determinar os vetores em termos de vetores unitários, podemos somar e subtrair os vetores ~a e ~b. (a) ~a + ~b: ~a + ~b = (4,0 m)̂i− (3,0 m)ĵ + (1,0 m)k̂ + (−1,0 m)̂i+ (1,0 m)ĵ + (4,0 m)k̂ ~a + ~b = (4,0 - 1,0)̂i + (−3,0 + 1,0)ĵ + (1,0 + 4,0)k̂ ~a + ~b = (3,0)̂i - (2,0)ĵ + (5,0)k̂ (b) ~a - ~b: ~a - ~b = (4,0 m)̂i− (3,0 m)ĵ + (1,0 m)k̂ - (−1,0 m)̂i- (1,0 m)ĵ - (4,0 m)k̂ ~a - ~b = (4,0 + 1,0)̂i + (−3,0 - 1,0)ĵ + (1,0 - 4,0)k̂ ~a - ~b = (5,0)̂i - (−4,0)ĵ + (−3,0)k̂ (c) Um terceiro vetor ~c, tal que ~a - ~b + ~c = 0: Para que ~a - ~b + ~c = 0, o vetor ~c deve ser igual a ~b - ~a: ~c = ~b - ~a ~c = (−1,0 m)̂i+ (1,0 m)ĵ + (4,0 m)k̂ - (4,0 m)̂i+ (3,0 m)ĵ - (1,0 m)k̂ ~c = (−1,0 - 4,0)̂i + (1,0 - 3,0)ĵ + (4,0 - 1,0)k̂ ~c = (−5,0)̂i + (−2,0)ĵ + (3,0)k̂ Espero que isso ajude!

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