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Let a and b be real numbers. Find all vectors left angle 1 comma a comma b right angle orthogonal to left angle 1 comma 8 comma 1 right angle.

Respuesta :

aramisdegaula1977

Answer:

[tex]A = (1, a, -1-8a)[/tex]. a and b are reals numbers.

Step-by-step explanation:

Let the vectors A = (1, a, b) and B = (1, 8, 1). If we assume that A and B are orthogonal vectors, then the scalar product between a and B is zero. Thus:

[tex]A \bullet B = (1, a, b) \bullet (1, 8, 1) = 1 + 8a + b = 0\\b = - 1 - 8a[/tex]

All vectors A orthogonal to vector B = (1, 8, 1) are given by: [tex]A = (1, a, -1-8a)[/tex]. a and b are reals numbers.

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