A body moves 6,m north,8,m east,and 10,m vert | vedclass

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Question

(A) Let the initial position be the origin $(0, 0, 0)$.Moving $6\,m$ north corresponds to the $y$-axis,$8\,m$ east corresponds to the $x$-axis,and $10

Vedclass · Accepted Answer

$10\sqrt{2}\,m$

Vedclass · Answer

(A) Let the initial position be the origin $(0, 0, 0)$.Moving $6\,m$ north corresponds to the $y$-axis,$8\,m$ east corresponds to the $x$-axis,and $10\,m$ vertically upwards corresponds to the $z$-axis.The position vector of the body is $\vec{r} = 8\hat{i} + 6\hat{j} + 10\hat{k}$.The magnitude of the resultant displacement is given by $r = |\vec{r}| = \sqrt{x^2 + y^2 + z^2}$.Substituting the values: $r = \sqrt{8^2 + 6^2 + 10^2}$.$r = \sqrt{64 + 36 + 100} = \sqrt{200}$.$r = \sqrt{100 	imes 2} = 10\sqrt{2}\,m$.

$A$ body moves $6\,m$ north,$8\,m$ east,and $10\,m$ vertically upwards. What is its resultant displacement from the initial position?

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