text: Precisely! Scalar multiplication is very simple. We just have to multiply the x- and the y-components ($$3$$ and $$-2$$ respectively) by $$5$$, that's it!
  If $$\vec{A} = \hat{i} - \hat{j}$$, $$\vec{B} = - 2 \hat{i} + 3 \hat{j}$$ and $$\vec{C} = 2 \hat{i} + \hat{j}$$, what is $$3 \vec{A} - 2 \vec{B} + 4 \vec{C}$$?
  • $$15 \hat{i} - 5 \hat{j}$$
  • $$9 \hat{i} + 7 \hat{j}$$
  • $$-9 \hat{i} - 7 \hat{j}$$
  • $$12 \hat{i} - 5 \hat{j}$$
explanation: The document describes a math problem involving vector operations. It provides vectors \(\vec{A}\), \(\vec{B}\), and \(\vec{C}\) and asks for the result of the expression \(3 \vec{A} - 2 \vec{B} + 4 \vec{C}\). The document also lists multiple-choice options for the answer.
distilabel_metadata.content: Evaluate the user given text extract and determine if it contains a math question and optionally and answer to this question.
  
  Output rules:
  
  1. Briefly describe the document and mention if it contains a question or a question and answer.
  2. Finalize the output with: Label: no-question,question,question-and-answer,multiple-question,multiple-question-and-answer
distilabel_metadata.role: system
distilabel_metadata.content: Precisely! Scalar multiplication is very simple. We just have to multiply the x- and the y-components ($$3$$ and $$-2$$ respectively) by $$5$$, that's it!
  If $$\vec{A} = \hat{i} - \hat{j}$$, $$\vec{B} = - 2 \hat{i} + 3 \hat{j}$$ and $$\vec{C} = 2 \hat{i} + \hat{j}$$, what is $$3 \vec{A} - 2 \vec{B} + 4 \vec{C}$$?
  • $$15 \hat{i} - 5 \hat{j}$$
  • $$9 \hat{i} + 7 \hat{j}$$
  • $$-9 \hat{i} - 7 \hat{j}$$
  • $$12 \hat{i} - 5 \hat{j}$$
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The document describes a math problem involving vector operations. It provides vectors \(\vec{A}\), \(\vec{B}\), and \(\vec{C}\) and asks for the result of the expression \(3 \vec{A} - 2 \vec{B} + 4 \vec{C}\). The document also lists multiple-choice options for the answer.
  
  Label: question-and-answer