37900149
Description
Quiz by BOTE FÉ NA MATEMÁTICA, updated more than 1 year ago
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Created by BOTE FÉ NA MATEMÁTICA
over 1 year ago
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Question 1
Question
Sejam \(\vec{a} = (2, -1, 5)\) e \(\vec{b} = -\vec{i} - \vec{j}\). Calcule \(\vec{a}.\vec{b}\).
Answer
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-1
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0
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1
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2
Question 2
Question
Dados os vetores \(\vec{u} = (2, -3, -1)\) e \(\vec{v} = (1, -1, 4)\), marque a alternativa que fornece o valor de \((\vec{u} +3\vec{v}).(\vec{v} - 2\vec{u})\).
Answer
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21
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20
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22
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-21
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0
Question 3
Question
Dados os vetores \(\vec{u} = (2, -3, -1)\) e \(\vec{v} = (1, -1, 4)\), marque a alternativa que fornece o valor de \(2\vec{u}.( -\vec{v})\).
Answer
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-2
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2
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0
-
1
Question 4
Question
Dados os pontos A(4, 0, -1) e B(2, -2, 1) e os vetores \(\vec{u}=(2, 1, 1)\) e \(\vec{v}=(-1, -2, 3)\), obter o vetor \(\vec{w}\) tal que \(3\vec{w} + 2\vec{v} = \vec{w} + (\vec{AB}.\vec{u})\vec{v}\).
Answer
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\(\vec{w} = (3, 6, -9)\)
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\(\vec{w} = (3, 6, 9)\)
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\(\vec{w} = (-3, 6, -9)\)
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\(\vec{w} = (3, -6, -9)\)
Question 5
Question
Determine o vetor \(\vec{v}\), paralelo ao vetor \(\vec{u} = (2, -1, 3)\), tal que \(\vec{v}.\vec{u} = -42\).
Answer
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\(\vec{v} = (-6, 3, -9)\).
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\(\vec{v} = (6, 3, -9)\).
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\(\vec{v} = (-6, 3, 9)\).
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\(\vec{v} = (-6, -3, -9)\).
Question 6
Question
Sejam \(\vec{a}\) e \(\vec{b}\) vetores tais que \(\|\vec{a}\| = 5\) e \(\|\vec{b}\| = 2\) e \((\vec{a}, \vec{b}) = \frac{\pi}{6}\). Calcule \(\vec{a}.\vec{b}\).
Answer
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\(5\sqrt{3}\)
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\(5\sqrt{2}\)
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\(5\)
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\(10\sqrt{3}\)
Question 7
Question
Determine o ângulo entre os vetores \(\vec{a} = (2, -1, -1)\) e \(\vec{b} = (-1, -1, 2)\).
Answer
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\(120°\)
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\(60°\)
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\(30°\)
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\(45°\)
Question 8
Question
Qual deve ser o valor de \(x\) para que os vetores \(\vec{a} = x\vec{i}+2\vec{j}-4\vec{k}\) e \(\vec{b} = 2\vec{i} + (1-2x)\vec{j} + 3\vec{k}\) sejam ortogonais?
Answer
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-5
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5
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0
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1
-
-1
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