Physics - Vectors Question with Solution | TestHub

Given,$\overrightarrow{\mathrm{A}}=7\hat{\mathrm{i}}+6\hat{\mathrm{j}}$

Let$\overrightarrow{\mathrm{B}}={\mathrm{b}}_1\hat{\mathrm{i}}+{\mathrm{b}}_2\hat{\mathrm{j}}$......(i)

Given that,$\overrightarrow{\mathrm{A}}+\overrightarrow{\mathrm{B}}=11\hat{\mathrm{i}}+9\hat{\mathrm{j}}$

Or$\left(7+{\mathrm{b}}_1\right)\hat{\mathrm{i}}+\left(6+{\mathrm{b}}_2\right)\hat{\mathrm{j}}=11\hat{\mathrm{i}}+9\hat{\mathrm{j}}$

Comparing the scalar component of$\hat{\mathrm{i}}$and$\hat{\mathrm{j}}$

$7+{\mathrm{b}}_1=11$and$\mathrm{ }6+{\mathrm{b}}_2=9$

$\Rightarrow {\mathrm{b}}_1=4$and${\mathrm{b}}_2=3$

$\therefore$From Equation. (i),

$\overrightarrow{\mathrm{B}}=4\hat{\mathrm{i}}+3\hat{\mathrm{j}}$

$\left|\overrightarrow{\mathrm{B}}\right|=\sqrt{4^2+3^2}=\sqrt{25}=5$