38264267
Description
Quiz by BOTE FÉ NA MATEMÁTICA, updated more than 1 year ago
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Created by BOTE FÉ NA MATEMÁTICA
about 2 years ago
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Question 1
Question
Marque a alternativa que fornece as equações paramétricas e simétricas da reta que passa pelo ponto A=(1, 2, 2) cujo vetor diretor é \(\vec{v} = (3, -1, 1)\).
Answer
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\(\begin{array}{l} x(t) = 1 + 3t\\ y(t) = 2 - t\\ z(t) = 2 + t \end{array}\); e \(\frac{x-1}{3} = \frac{y-2}{-1} = z-2\)
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\(\begin{array}{l} x(t) = 1 + 3t\\ y(t) = 2 - t\\ z(t) = 2 + t \end{array}\); e \(\frac{x-1}{3} = \frac{y-2}{1} = z-2\)
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\(\begin{array}{l} x(t) = 1 + 3t\\ y(t) = 2 - t\\ z(t) = 2 + t \end{array}\); e \(\frac{x+1}{3} = \frac{y-2}{-1} = z-2\)
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\(\begin{array}{l} x(t) = 1 + 3t\\ y(t) = 2 +t\\ z(t) = 2 - t \end{array}\); e \(\frac{x-1}{3} = \frac{y-2}{-1} = z-2\)
Question 2
Question
Marque a alternativa que fornece as equações paramétricas e simétricas da reta que passa pelos pontos \(P_1 = (1, 2, 3)\) e \(P_2 = (5, 0, 6)\).
Answer
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\(\begin{array}{l} x(t) = 1 + 4t\\ y(t) = 2 -2t\\ z(t) = 3 + 3t \end{array}\); e \(\frac{x-1}{4} = \frac{y-2}{-2} = \frac{z-3}{3}\)
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\(\begin{array}{l} x(t) = 1 + 4t\\ y(t) = 2 -2t\\ z(t) = 3 + 3t \end{array}\); e \(\frac{x+1}{4} = \frac{y-2}{-2} = \frac{z-3}{3}\)
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\(\begin{array}{l} x(t) = 1 + 4t\\ y(t) = 2 +2t\\ z(t) = 3 + 3t \end{array}\); e \(\frac{x-1}{4} = \frac{y+2}{-2} = \frac{z-3}{3}\)
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\(\begin{array}{l} x(t) = 1 + 4t\\ y(t) = 2 -2t\\ z(t) = 3 - 3t \end{array}\); e \(\frac{x-1}{4} = \frac{y-2}{2} = \frac{z-3}{3}\)
Question 3
Question
Marque a alternativa que fornece as equações paramétricas da reta \(x-1 = \frac{5y +4}{2}=-6z+9\).
Answer
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\(\begin{array}{l} x(t) = 1 + t\\ y(t) = -\frac{4}{5} +\frac{2}{5}t\\ z(t) = \frac{3}{2} -\frac{1}{6}t \end{array}\)
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\(\begin{array}{l} x(t) = 1 + t\\ y(t) = -4 +2t\\ z(t) = \frac{3}{2} -\frac{1}{6}t \end{array}\)
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\(\begin{array}{l} x(t) = 1 + 2t\\ y(t) = -\frac{4}{5} +\frac{2}{5}t\\ z(t) = \frac{3}{2} -\frac{1}{6}t \end{array}\)
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\(\begin{array}{l} x(t) = 1 + t\\ y(t) = -\frac{4}{5} -\frac{2}{5}t\\ z(t) = \frac{3}{2} +\frac{1}{6}t \end{array}\)
Question 4
Question
Obtenha as equações simétricas da reta \(x=2-s\), \(y=4\), \(z=3s\).
Answer
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\(\frac{x-2}{-1} = \frac{z}{3}\); y=4.
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\(\frac{x-2}{-1} =\frac{y-4}{1} \frac{z}{3}\)
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\(\frac{x+2}{1} = \frac{z}{3}\); y=4.
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\(\frac{x-2}{1} = \frac{z}{3}\); y=4.
Question 5
Question
Marque a alternativa que fornece um ponto e um vetor diretor da reta \(\begin{array}{l}
x(t) = 1 -2t\\
y(t) =-5 + t\\
z(t) = 2 + 4t
\end{array}\).
Answer
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P = (1, -5, 2) e \(\vec{v} = (-2, 1, 4)\)
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P = (1, -5, 2) e \(\vec{v} = (-2, 3, 4)\)
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P = (1, 5, 2) e \(\vec{v} = (-2, 1, 4)\)
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P = (1, 5, 2) e \(\vec{v} = (2, 1, 4)\)
Question 6
Question
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 \(r_2: \begin{array}{l}
x(t) = 1 + 3s\\
y(t) = s\\
z(t) = -7 + 2s
\end{array}\)
Answer
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\(\begin{array}{l} x(t) = 4n\\ y(t) = 16n\\ z(t) = -14n \end{array}\)
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\(\begin{array}{l} x(t) = 2n\\ y(t) = 16n\\ z(t) = 14n \end{array}\)
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\(\begin{array}{l} x(t) = 4n\\ y(t) = 4n\\ z(t) = -14n \end{array}\)
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\(\begin{array}{l} x(t) = 4n\\ y(t) = n\\ z(t) = -n \end{array}\)
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