The vector projection of a vector 3hat i + 4h | vedclass

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(D) The vector is given by $\vec{A} = 3\hat{i} + 0\hat{j} + 4\hat{k}$.To find the projection of a vector $\vec{A}$ on a unit vector $\hat{n}$,we use t

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(D) The vector is given by $\vec{A} = 3\hat{i} + 0\hat{j} + 4\hat{k}$.To find the projection of a vector $\vec{A}$ on a unit vector $\hat{n}$,we use the dot product $\vec{A} \cdot \hat{n}$.The $Y$-axis is represented by the unit vector $\hat{j}$.Therefore,the projection is $(3\hat{i} + 0\hat{j} + 4\hat{k}) \cdot \hat{j} = 3(\hat{i} \cdot \hat{j}) + 0(\hat{j} \cdot \hat{j}) + 4(\hat{k} \cdot \hat{j})$.Since $\hat{i} \cdot \hat{j} = 0$,$\hat{j} \cdot \hat{j} = 1$,and $\hat{k} \cdot \hat{j} = 0$,the projection is $0 + 0 + 0 = 0$.

The vector projection of a vector $3\hat i + 4\hat k$ on the $Y$-axis is

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