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  • Provide solution for RD Sharma maths class 12 chapter 22 Algebra of Vectors exercise Fill in the blanks question 2

Provide solution for RD Sharma maths class 12 chapter 22 Algebra of Vectors exercise Fill in the blanks question 2

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Answer:- \overrightarrow{A C}=\vec{a}+\vec{b}, \overrightarrow{B D}=\vec{b}+\vec{a}

Hint:- To solve this equation ,we use right angle triangle formula.

Given:- In a parallelogram \mathrm{ABCD} \text { If } \overrightarrow{A B}=a \text { and } \overrightarrow{B C}=b \text {, then } \overrightarrow{A C}=\ldots \text { and } \overrightarrow{B D}=\ldots

Solution:- In \Delta ABC

According to right triangle

\begin{aligned} &\overrightarrow{A B}+\overrightarrow{B C}=\overrightarrow{A C}\\\\ &\vec{a}+\vec{b}=\overrightarrow{A C}\\\\ &\overrightarrow{A C}=\vec{a}+\vec{b}\\\\ &\text { In } \Delta B D A \end{aligned}

According to right triangle

\begin{aligned} &\overrightarrow{A B}+\overrightarrow{B D}=\overrightarrow{A D} \\\\ &\vec{a}+\overrightarrow{B D}=\vec{b} \\\\ &\overrightarrow{B D}=\vec{b}-\vec{a} \end{aligned}

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