The projection of vector vec{a} = hat{i} + 2h | vedclass

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(D) The projection of vector $\vec{a}$ on vector $\vec{b}$ is given by the formula: $	ext{Projection} = \frac{\vec{a} \cdot \vec{b}}{|\vec{b}|}$.Give

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$\frac{10}{\sqrt{17}}$

Vedclass · Answer

(D) The projection of vector $\vec{a}$ on vector $\vec{b}$ is given by the formula: $	ext{Projection} = \frac{\vec{a} \cdot \vec{b}}{|\vec{b}|}$.Given $\vec{a} = \hat{i} + 2\hat{j} + \hat{k}$ and $\vec{b} = 2\hat{i} + 3\hat{j} + 2\hat{k}$.First,calculate the dot product $\vec{a} \cdot \vec{b} = (1)(2) + (2)(3) + (1)(2) = 2 + 6 + 2 = 10$.Next,calculate the magnitude of $\vec{b}$: $|\vec{b}| = \sqrt{2^2 + 3^2 + 2^2} = \sqrt{4 + 9 + 4} = \sqrt{17}$.Therefore,the projection is $\frac{10}{\sqrt{17}}$.

The projection of vector $\vec{a} = \hat{i} + 2\hat{j} + \hat{k}$ on vector $\vec{b} = 2\hat{i} + 3\hat{j} + 2\hat{k}$ is . . . . . . .

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