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  • Explain solution RD Sharma class 12 chapter 22 Algebra of Vectors exercise Multiple choice question 16 maths

Explain solution RD Sharma class 12 chapter 22 Algebra of Vectors exercise Multiple choice question 16 maths

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Answer: 2 \overrightarrow{A B}

Hint: AC-BD=?

Given: ABCD is parallelogram with AC and BS as diagonal

Solution: ABCD is parallelogram So A B\|C D\; \&\; A D\| B C

            \overrightarrow{A C}=\overrightarrow{A B}-\overrightarrow{B C}            (Subtraction theorem)

            \overrightarrow{B D}=\overrightarrow{B A}-\overrightarrow{A D}            (Subtraction theorem)

            \begin{aligned} &\overrightarrow{A C}-\overrightarrow{B D}=\overrightarrow{A B}-\overrightarrow{B C}-\overrightarrow{B A}+\overrightarrow{A D}\\\\ &=\overrightarrow{A B}-\overrightarrow{B C}+\overrightarrow{A B}+\overrightarrow{B C} \quad\quad\quad\quad\quad(A B\|C D\; \& \; A D\| B C) \end{aligned}

             =   2 \overrightarrow{A B}

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