Find the projection of the vector vec{a} = 2h | vedclass

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

Vedclass · Accepted Answer

$\frac{5}{3} \sqrt{6}$

Vedclass · Answer

(B) The projection of vector $\vec{a}$ on the vector $\vec{b}$ is given by the formula: $	ext{Projection} = \frac{\vec{a} \cdot \vec{b}}{|\vec{b}|}$.First,calculate the dot product $\vec{a} \cdot \vec{b}$:$\vec{a} \cdot \vec{b} = (2)(1) + (3)(2) + (2)(1) = 2 + 6 + 2 = 10$.Next,calculate the magnitude of vector $\vec{b}$:$|\vec{b}| = \sqrt{(1)^2 + (2)^2 + (1)^2} = \sqrt{1 + 4 + 1} = \sqrt{6}$.Finally,the projection is:$\frac{10}{\sqrt{6}} = \frac{10 	imes \sqrt{6}}{\sqrt{6} 	imes \sqrt{6}} = \frac{10\sqrt{6}}{6} = \frac{5}{3} \sqrt{6}$.

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

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