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

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Question

(C) Let $\vec{a} = \hat{i} - 2\hat{j} + 3\hat{k}$ and $\vec{b} = 3\hat{i} - 2\hat{j} + \hat{k}$.The projection vector of $\vec{a}$ on $\vec{b}$ is giv

Vedclass · Accepted Answer

$\frac{15}{7}\hat{i} - \frac{10}{7}\hat{j} + \frac{5}{7}\hat{k}$

Vedclass · Answer

(C) Let $\vec{a} = \hat{i} - 2\hat{j} + 3\hat{k}$ and $\vec{b} = 3\hat{i} - 2\hat{j} + \hat{k}$.The projection vector of $\vec{a}$ on $\vec{b}$ is given by the formula: $\left( \frac{\vec{a} \cdot \vec{b}}{|\vec{b}|^2} ight) \vec{b}$.First,calculate the dot product: $\vec{a} \cdot \vec{b} = (1)(3) + (-2)(-2) + (3)(1) = 3 + 4 + 3 = 10$.Next,calculate the magnitude squared of $\vec{b}$: $|\vec{b}|^2 = 3^2 + (-2)^2 + 1^2 = 9 + 4 + 1 = 14$.Now,substitute these values into the formula: $	ext{Projection vector} = \frac{10}{14} (3\hat{i} - 2\hat{j} + \hat{k}) = \frac{5}{7} (3\hat{i} - 2\hat{j} + \hat{k}) = \frac{15}{7}\hat{i} - \frac{10}{7}\hat{j} + \frac{5}{7}\hat{k}$.Thus,the correct option is $C$.

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

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