If a = 4 hat{i} + 6 hat{j},b = 3 hat{j} + 4 h | vedclass

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(A) Given: $a = 4 \hat{i} + 6 \hat{j}$ and $b = 3 \hat{j} + 4 \hat{k}$.The projection vector of $a$ on $b$ is given by the formula $c = \left( \frac{a

Vedclass · Accepted Answer

$\frac{18}{25} b, \frac{18}{5}$

Vedclass · Answer

(A) Given: $a = 4 \hat{i} + 6 \hat{j}$ and $b = 3 \hat{j} + 4 \hat{k}$.The projection vector of $a$ on $b$ is given by the formula $c = \left( \frac{a \cdot b}{|b|^2} ight) b$.First,calculate the dot product $a \cdot b = (4 \hat{i} + 6 \hat{j}) \cdot (3 \hat{j} + 4 \hat{k}) = (4 	imes 0) + (6 	imes 3) + (0 	imes 4) = 18$.Next,calculate $|b|^2 = 3^2 + 4^2 = 9 + 16 = 25$.Thus,$c = \left( \frac{18}{25} ight) b$.Now,calculate the magnitude $|c| = \left| \frac{18}{25} ight| |b| = \frac{18}{25} 	imes \sqrt{3^2 + 4^2} = \frac{18}{25} 	imes 5 = \frac{18}{5}$.Therefore,$c = \frac{18}{25} b$ and $|c| = \frac{18}{5}$.

If $a = 4 \hat{i} + 6 \hat{j}$,$b = 3 \hat{j} + 4 \hat{k}$,and $c$ is the projection vector of $a$ on $b$,then $c$ and $|c|$ respectively are

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