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}
The text passage contains a mathematical question from a specific textbook and exercise, along with a detailed solution that answers the question.
single_question_with_answer
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
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}
user
The text passage contains a mathematical question from a specific textbook and exercise, along with a detailed solution that answers the question.

TYPE: SINGLE_QUESTION_WITH_ANSWER