The shortest distance of the point (a, b, c) | vedclass

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Question

(B) The shortest distance of a point $P(a, b, c)$ from the $x$-axis is the perpendicular distance from the point to the axis.Since any point on the $x

Vedclass · Accepted Answer

$\sqrt{b^2 + c^2}$

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(B) The shortest distance of a point $P(a, b, c)$ from the $x$-axis is the perpendicular distance from the point to the axis.Since any point on the $x$-axis has coordinates of the form $(x, 0, 0)$,the projection of point $P(a, b, c)$ onto the $x$-axis is $P'(a, 0, 0)$.The distance formula between $P(a, b, c)$ and $P'(a, 0, 0)$ is given by:$d = \sqrt{(a - a)^2 + (b - 0)^2 + (c - 0)^2}$$d = \sqrt{0^2 + b^2 + c^2}$$d = \sqrt{b^2 + c^2}$Therefore,the shortest distance is $\sqrt{b^2 + c^2}$.

The shortest distance of the point $(a, b, c)$ from the $x$-axis is

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