The magnitude of x and y components of → A are 7 and 6...

Given, \overset{→}{A} = 7\overset{^}{i} + 6\overset{^}{j}

Let \overset{→}{B} = {b}_{1}\overset{^}{i} + {b}_{2}\overset{^}{j} ......(i)

Given that, \overset{→}{A} + \overset{→}{B} = 11\overset{^}{i} + 9\overset{^}{j}

Or \left(7 + {b}_{1}\right)\overset{^}{i} + \left(6 + {b}_{2}\right)\overset{^}{j} = 11\overset{^}{i} + 9\overset{^}{j}$<br/><br/>Comparing the scalar component of$\overset{^}{i}$and$\overset{^}{j}$<br/><br/>$7 + {b}_{1} = 11$and$6 + {b}_{2} = 9$<br/><br/>$⇒ {b}_{1} = 4$and${b}_{2} = 3$<br/><br/>$∴$From Equation. (i),<br/><br/>$\overset{→}{B} = 4\overset{^}{i} + 3\overset{^}{j}$<br/><br/>\left|\overset{→}{B}\right| = \sqrt{{4}^{2} + {3}^{2}} = \sqrt{25} = 5$