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(A) The projection of a vector $\vec{a}$ along a vector $\vec{b}$ is given by the formula $\frac{\vec{a} \cdot \vec{b}}{|\vec{b}|}$.Let $\vec{a} = i +

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$1$

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(A) The projection of a vector $\vec{a}$ along a vector $\vec{b}$ is given by the formula $\frac{\vec{a} \cdot \vec{b}}{|\vec{b}|}$.Let $\vec{a} = i + j + k$ and $\vec{b} = j$.First,calculate the dot product $\vec{a} \cdot \vec{b} = (i + j + k) \cdot j = (1)(0) + (1)(1) + (1)(0) = 1$.Next,calculate the magnitude of vector $\vec{b}$,which is $|\vec{b}| = |j| = 1$.Therefore,the projection is $\frac{\vec{a} \cdot \vec{b}}{|\vec{b}|} = \frac{1}{1} = 1$.

The projection of the vector $i+j+k$ along the vector $j$ is

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