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Algebra of Vectors — Maths STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceMathsAlgebra of Vectors2 Marks
Question
If $\vec{\text{a}}\text{ and }\vec{\text{b}}$ represent two adjacent sides of a parallelogram, then write vectors representing its diagonals.
✓

Answer

Let $\vec{\text{a}}\text{ and }\vec{\text{b}}$ represents two adjacent sides of a parallelogram ABCD.
$\therefore$ AB = DC and AD = BC
$\Rightarrow\ \overrightarrow{\text{DC}}=\overrightarrow{\text{AB}}=\vec{\text{a}}$ and $\Rightarrow\ \overrightarrow{\text{AD}}=\overrightarrow{\text{BC}}=\vec{\text{b}}$
In $\triangle\text{ABC}$
$\overrightarrow{\text{AB}}+\overrightarrow{\text{BC}}=\overrightarrow{\text{AC}}$
$\Rightarrow\ \vec{\text{a}}+\vec{\text{b}}=\overrightarrow{\text{AC}}$
In $\triangle\text{ABD}$
$\ \overrightarrow{\text{AD}}+\overrightarrow{\text{DB}}=\overrightarrow{\text{AB}}$
$\Rightarrow\ \vec{\text{b}}+\overrightarrow{\text{DB}}=\vec{\text{a}}$
$\Rightarrow\ \overrightarrow{\text{DB}}=\vec{\text{a}}-\vec{\text{b}}$

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