If vector vec{a} = 2hat{i} - 3hat{j} + 6hat{k | vedclass

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(B) The projection of vector $\vec{a}$ on vector $\vec{b}$ is given by $\frac{\vec{a} \cdot \vec{b}}{|\vec{b}|}$.The projection of vector $\vec{b}$ on

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$\frac{7}{3}$

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(B) The projection of vector $\vec{a}$ on vector $\vec{b}$ is given by $\frac{\vec{a} \cdot \vec{b}}{|\vec{b}|}$.The projection of vector $\vec{b}$ on vector $\vec{a}$ is given by $\frac{\vec{b} \cdot \vec{a}}{|\vec{a}|}$.Therefore,the required ratio is $\frac{\frac{\vec{a} \cdot \vec{b}}{|\vec{b}|}}{\frac{\vec{b} \cdot \vec{a}}{|\vec{a}|}} = \frac{|\vec{a}|}{|\vec{b}|}$.Given $\vec{a} = 2\hat{i} - 3\hat{j} + 6\hat{k}$,we have $|\vec{a}| = \sqrt{2^2 + (-3)^2 + 6^2} = \sqrt{4 + 9 + 36} = \sqrt{49} = 7$.Given $\vec{b} = -2\hat{i} + 2\hat{j} - \hat{k}$,we have $|\vec{b}| = \sqrt{(-2)^2 + 2^2 + (-1)^2} = \sqrt{4 + 4 + 1} = \sqrt{9} = 3$.Thus,the required ratio is $\frac{7}{3}$.

If vector $\vec{a} = 2\hat{i} - 3\hat{j} + 6\hat{k}$ and vector $\vec{b} = -2\hat{i} + 2\hat{j} - \hat{k},$ then $\frac{\text{Projection of vector } \vec{a} \text{ on vector } \vec{b}}{\text{Projection of vector } \vec{b} \text{ on vector } \vec{a}} = $

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