text: Provide solution for RD sharma maths class 12 chapter 24 Vector or cross product exercise Fill in the blanks question 6
  
  =4
  
  Hint: Use formula
  
  \begin{aligned} &|\vec{a} \times \vec{b}|^{2}+|\vec{a} \cdot \vec{b}|^{2}=|a|^{2}|b|^{2} \\ \end{aligned}
  
  Given:
  
  \begin{aligned} &\vec{a}=\hat{i}-{ }^{2} \\ &\vec{b}=\hat{j}+\hat{k} \\ \end{aligned}
  
  \begin{aligned} &|\vec{a}|=\sqrt{(1)^{2}+(-1)^{2}}=\sqrt{2} \\ &|\vec{b}|=\sqrt{(1)^{2}+(1)^{2}}=\sqrt{2} \\ \end{aligned}
  
  Using formula
  
  \begin{aligned} &|\vec{a} \times \vec{b}|^{2}+|\vec{a} \cdot \vec{b}|^{2}=|a|^{2}|b|^{2} \\ &=(\sqrt{2})^{2}(\sqrt{2})^{2} \\ &=(2)(2) \\ &=4 \end{aligned}
explanation: The document provides a math question from RD Sharma's class 12 textbook, specifically from chapter 24 on Vector or Cross Product. It includes a fill-in-the-blank question and a detailed solution using the given formula and vectors. The solution is provided step-by-step, leading to the final answer of 4.
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: Provide solution for RD sharma maths class 12 chapter 24 Vector or cross product exercise Fill in the blanks question 6
  
  =4
  
  Hint: Use formula
  
  \begin{aligned} &|\vec{a} \times \vec{b}|^{2}+|\vec{a} \cdot \vec{b}|^{2}=|a|^{2}|b|^{2} \\ \end{aligned}
  
  Given:
  
  \begin{aligned} &\vec{a}=\hat{i}-{ }^{2} \\ &\vec{b}=\hat{j}+\hat{k} \\ \end{aligned}
  
  \begin{aligned} &|\vec{a}|=\sqrt{(1)^{2}+(-1)^{2}}=\sqrt{2} \\ &|\vec{b}|=\sqrt{(1)^{2}+(1)^{2}}=\sqrt{2} \\ \end{aligned}
  
  Using formula
  
  \begin{aligned} &|\vec{a} \times \vec{b}|^{2}+|\vec{a} \cdot \vec{b}|^{2}=|a|^{2}|b|^{2} \\ &=(\sqrt{2})^{2}(\sqrt{2})^{2} \\ &=(2)(2) \\ &=4 \end{aligned}
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The document provides a math question from RD Sharma's class 12 textbook, specifically from chapter 24 on Vector or Cross Product. It includes a fill-in-the-blank question and a detailed solution using the given formula and vectors. The solution is provided step-by-step, leading to the final answer of 4.
  
  Label: question-and-answer