What will be the projection of vector vec{A} | vedclass

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(B) The projection of vector $\vec{A}$ on vector $\vec{B}$ is given by the formula: $	ext{Proj}_{\vec{B}} \vec{A} = \left( \frac{\vec{A} \cdot \vec{B

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$(\hat{i} + \hat{j})$

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(B) The projection of vector $\vec{A}$ on vector $\vec{B}$ is given by the formula: $	ext{Proj}_{\vec{B}} \vec{A} = \left( \frac{\vec{A} \cdot \vec{B}}{|\vec{B}|} ight) \hat{B}$,where $\hat{B}$ is the unit vector along $\vec{B}$.First,calculate the dot product: $\vec{A} \cdot \vec{B} = (1)(1) + (1)(1) + (1)(0) = 1 + 1 = 2$.Next,calculate the magnitude of $\vec{B}$: $|\vec{B}| = \sqrt{1^2 + 1^2} = \sqrt{2}$.Then,the unit vector $\hat{B} = \frac{\vec{B}}{|\vec{B}|} = \frac{\hat{i} + \hat{j}}{\sqrt{2}}$.Finally,substitute these values into the projection formula:$	ext{Proj}_{\vec{B}} \vec{A} = \left( \frac{2}{\sqrt{2}} ight) \left( \frac{\hat{i} + \hat{j}}{\sqrt{2}} ight) = \sqrt{2} \cdot \frac{\hat{i} + \hat{j}}{\sqrt{2}} = \hat{i} + \hat{j}$.

Column $I$	Column $II$
$(A) (A+B)$	$(p)$ North-east
$(B) (A-B)$	$(q)$ Vertically upwards
$(C) (A \times B)$	$(r)$ Vertically downwards
$(D) (A \times B) \times (A \times B)$	$(s)$ None

What will be the projection of vector $\vec{A} = \hat{i} + \hat{j} + \hat{k}$ on vector $\vec{B} = \hat{i} + \hat{j}$?

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