If overline{a} = 2 hat{i} + 3 hat{j} - 4 hat{ | vedclass

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(D) The projection of vector $\overline{b}$ in the direction of vector $\overline{a}$ is given by the formula: $	ext{Projection} = \frac{\overline{a}

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$\frac{3}{\sqrt{29}}$

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(D) The projection of vector $\overline{b}$ in the direction of vector $\overline{a}$ is given by the formula: $	ext{Projection} = \frac{\overline{a} \cdot \overline{b}}{|\overline{a}|}$.First,calculate the dot product $\overline{a} \cdot \overline{b} = (2)(1) + (3)(-1) + (-4)(-1) = 2 - 3 + 4 = 3$.Next,calculate the magnitude of $\overline{a}$: $|\overline{a}| = \sqrt{2^2 + 3^2 + (-4)^2} = \sqrt{4 + 9 + 16} = \sqrt{29}$.Therefore,the projection is $\frac{3}{\sqrt{29}}$.

If $\overline{a} = 2 \hat{i} + 3 \hat{j} - 4 \hat{k}$ and $\overline{b} = \hat{i} - \hat{j} - \hat{k}$,then the projection of $\overline{b}$ in the direction of $\overline{a}$ is

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