When vector $$\vec{A} = 2\hat{i} + 3\hat{j} + 2\hat{k}$$ is subtracted from vector $$\vec{B}$$, it gives a vector equal to $$2\hat{j}$$. Then the magnitude of vector $$\vec{B}$$ will be:

Given: $$\vec{B} - \vec{A} = 2\hat{j}$$

$$\vec{A} = 2\hat{i} + 3\hat{j} + 2\hat{k}$$

$$\vec{B} = \vec{A} + 2\hat{j} = 2\hat{i} + 3\hat{j} + 2\hat{k} + 2\hat{j} = 2\hat{i} + 5\hat{j} + 2\hat{k}$$

$$|\vec{B}| = \sqrt{2^2 + 5^2 + 2^2} = \sqrt{4 + 25 + 4} = \sqrt{33}$$

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