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}