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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(4, -1), B(1, 3)
Find $\Big|\overrightarrow{\text{AB}}\Big|$
✓

Answer

Here, A = (4, -1) B = (1, 3) Position vector of $\text{A}=4\hat{\text{i}}-\hat{\text{j}}$ Position vector of $\text{B}=\hat{\text{i}}+3\hat{\text{j}}$ $\overrightarrow{\text{AB}}$ = Position vector of B - Position vector of A$=\big(\hat{\text{i}}+3\hat{\text{j}}\big)-\big(4\hat{\text{i}}-\hat{\text{j}}\big)$
$=\hat{\text{i}}+3\hat{\text{j}}-4\hat{\text{i}}+\hat{\text{j}}$
$\overrightarrow{\text{AB}}=-3\hat{\text{i}}+4\hat{\text{j}}$
$\Big|\overrightarrow{\text{AB}}\Big|=\sqrt{(-3)^2+(4)^2}$
$=\sqrt{9+16}$
$=\sqrt{25}$
$\Big|\overrightarrow{\text{AB}}\Big|=5$
$\overrightarrow{\text{AB}}=-3\hat{\text{i}}+4\hat{\text{j}}$

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