BOTE FÉ NA MATEMÁTICA
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Nessa atividade iremos trabalhar os conteúdos de retas e planos.

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BOTE FÉ NA MATEMÁTICA
Created by BOTE FÉ NA MATEMÁTICA about 2 years ago
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Lista de Exercícios Retas

Lista de Exercícios Retas

Question 1 of 6

1

Marque a alternativa que fornece as equações paramétricas e simétricas da reta que passa pelo ponto A=(1, 2, 2) cujo vetor diretor é \(\vec{v} = (3, -1, 1)\).

Select one of the following:

  • \(\begin{array}{l}
    x(t) = 1 + 3t\\
    y(t) = 2 - t\\
    z(t) = 2 + t
    \end{array}\); e \(\frac{x-1}{3} = \frac{y-2}{-1} = z-2\)

  • \(\begin{array}{l}
    x(t) = 1 + 3t\\
    y(t) = 2 - t\\
    z(t) = 2 + t
    \end{array}\); e \(\frac{x-1}{3} = \frac{y-2}{1} = z-2\)

  • \(\begin{array}{l}
    x(t) = 1 + 3t\\
    y(t) = 2 - t\\
    z(t) = 2 + t
    \end{array}\); e \(\frac{x+1}{3} = \frac{y-2}{-1} = z-2\)

  • \(\begin{array}{l}
    x(t) = 1 + 3t\\
    y(t) = 2 +t\\
    z(t) = 2 - t
    \end{array}\); e \(\frac{x-1}{3} = \frac{y-2}{-1} = z-2\)

Explanation

Question 2 of 6

1

Marque a alternativa que fornece as equações paramétricas e simétricas da reta que passa pelos pontos \(P_1 = (1, 2, 3)\) e \(P_2 = (5, 0, 6)\).

Select one of the following:

  • \(\begin{array}{l}
    x(t) = 1 + 4t\\
    y(t) = 2 -2t\\
    z(t) = 3 + 3t
    \end{array}\); e \(\frac{x-1}{4} = \frac{y-2}{-2} = \frac{z-3}{3}\)

  • \(\begin{array}{l}
    x(t) = 1 + 4t\\
    y(t) = 2 -2t\\
    z(t) = 3 + 3t
    \end{array}\); e \(\frac{x+1}{4} = \frac{y-2}{-2} = \frac{z-3}{3}\)

  • \(\begin{array}{l}
    x(t) = 1 + 4t\\
    y(t) = 2 +2t\\
    z(t) = 3 + 3t
    \end{array}\); e \(\frac{x-1}{4} = \frac{y+2}{-2} = \frac{z-3}{3}\)

  • \(\begin{array}{l}
    x(t) = 1 + 4t\\
    y(t) = 2 -2t\\
    z(t) = 3 - 3t
    \end{array}\); e \(\frac{x-1}{4} = \frac{y-2}{2} = \frac{z-3}{3}\)

Explanation

Question 3 of 6

1

Marque a alternativa que fornece as equações paramétricas da reta \(x-1 = \frac{5y +4}{2}=-6z+9\).

Select one of the following:

  • \(\begin{array}{l}
    x(t) = 1 + t\\
    y(t) = -\frac{4}{5} +\frac{2}{5}t\\
    z(t) = \frac{3}{2} -\frac{1}{6}t
    \end{array}\)

  • \(\begin{array}{l}
    x(t) = 1 + t\\
    y(t) = -4 +2t\\
    z(t) = \frac{3}{2} -\frac{1}{6}t
    \end{array}\)

  • \(\begin{array}{l}
    x(t) = 1 + 2t\\
    y(t) = -\frac{4}{5} +\frac{2}{5}t\\
    z(t) = \frac{3}{2} -\frac{1}{6}t
    \end{array}\)

  • \(\begin{array}{l}
    x(t) = 1 + t\\
    y(t) = -\frac{4}{5} -\frac{2}{5}t\\
    z(t) = \frac{3}{2} +\frac{1}{6}t
    \end{array}\)

Explanation

Question 4 of 6

1

Obtenha as equações simétricas da reta \(x=2-s\), \(y=4\), \(z=3s\).

Select one of the following:

  • \(\frac{x-2}{-1} = \frac{z}{3}\); y=4.

  • \(\frac{x-2}{-1} =\frac{y-4}{1} \frac{z}{3}\)

  • \(\frac{x+2}{1} = \frac{z}{3}\); y=4.

  • \(\frac{x-2}{1} = \frac{z}{3}\); y=4.

Explanation

Question 5 of 6

1

Marque a alternativa que fornece um ponto e um vetor diretor da reta \(\begin{array}{l}
x(t) = 1 -2t\\
y(t) =-5 + t\\
z(t) = 2 + 4t
\end{array}\).

Select one of the following:

  • P = (1, -5, 2) e \(\vec{v} = (-2, 1, 4)\)

  • P = (1, -5, 2) e \(\vec{v} = (-2, 3, 4)\)

  • P = (1, 5, 2) e \(\vec{v} = (-2, 1, 4)\)

  • P = (1, 5, 2) e \(\vec{v} = (2, 1, 4)\)

Explanation

Question 6 of 6

1

Determine as equações paramétricas e simétricas da reta que passa pela origem e é ortogonal às retas \(r_1: \begin{array}{l}
x(t) = 2 + t\\
y(t) = 3 +5t\\
z(t) = 5 + 6t
\end{array}\) e \(r_2: \begin{array}{l}
x(t) = 1 + 3s\\
y(t) = s\\
z(t) = -7 + 2s
\end{array}\)

Select one of the following:

  • \(\begin{array}{l}
    x(t) = 4n\\
    y(t) = 16n\\
    z(t) = -14n
    \end{array}\)

  • \(\begin{array}{l}
    x(t) = 2n\\
    y(t) = 16n\\
    z(t) = 14n
    \end{array}\)

  • \(\begin{array}{l}
    x(t) = 4n\\
    y(t) = 4n\\
    z(t) = -14n
    \end{array}\)

  • \(\begin{array}{l}
    x(t) = 4n\\
    y(t) = n\\
    z(t) = -n
    \end{array}\)

Explanation

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