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Algebra of Vectors — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsAlgebra of Vectors3 Marks
Question
Express $\overrightarrow{\text{AB}}$ in terms of unit vectors $\hat{\text{i}}\text{ and }\hat{\text{j}}$, when the point is:A(-6, 3), B(-2, -5)
Find $\Big|\overrightarrow{\text{AB}}\Big|$
✓

Answer

Here, A = (-6, 3) B = (-2, -5) Position vector of $\text{A}=-6\hat{\text{i}}+3\hat{\text{j}}$ Position vector of $\text{B}=-2\hat{\text{i}}-5\hat{\text{j}}$ $\overrightarrow{\text{AB}}$ = Position vector of B - Position vector of A$=\big(-2\hat{\text{i}}-5\hat{\text{j}}\big)-\big(-6\hat{\text{i}}+3\hat{\text{j}}\big)$
$=-2\hat{\text{i}}-5\hat{\text{j}}+6\hat{\text{i}}-3\hat{\text{j}}$
$\overrightarrow{\text{AB}}=4\hat{\text{i}}-8\hat{\text{j}}$
$\Big|\overrightarrow{\text{AB}}\Big|=\sqrt{(4)^2+(-8)^2}$
$=\sqrt{16+64}$
$=\sqrt{80}$
$=\sqrt{16\times5}$ $=4\sqrt5$$\Big|\overrightarrow{\text{AB}}\Big|=4\sqrt5$
$\overrightarrow{\text{AB}}=4\hat{\text{i}}-8\hat{\text{j}}$

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