When vector → A = 2 ^ i + 3 ^ j + 2 ^ k is subtracted from vector →...

It is given that \overset{\to}{A} = 2\overset{^}{i} + 3\overset{^}{j} + 2\overset{^}{k}.

By the given condition,

\overset{\to}{B} - ( 2\overset{^}{i} + 3\overset{^}{j} + 2\overset{^}{k} ) = 2\overset{^}{j}

⇒ \overset{\to}{B} = 2\overset{^}{i} + 5\overset{^}{j} + 2\overset{^}{k}

The magnitude is given by the formula,\left|\overset{\to}{B}\right| = \sqrt{{B}^{2}x + {B}^{2}y + {B}^{2}z}$<br />$⇒ | \overset{\to}{B} | = \sqrt{4 + 25 + 4} = \sqrt{33}