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

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Question

(A) The distance of a point $P(a, b, c)$ from the $z$-axis is the distance between $P(a, b, c)$ and the foot of the perpendicular from $P$ onto the $z

Vedclass · Accepted Answer

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

Vedclass · Answer

(A) The distance of a point $P(a, b, c)$ from the $z$-axis is the distance between $P(a, b, c)$ and the foot of the perpendicular from $P$ onto the $z$-axis. The coordinates of the foot of the perpendicular from $P(a, b, c)$ onto the $z$-axis are $(0, 0, c)$. Using the distance formula $d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2 + (z_2 - z_1)^2}$,we get: $d = \sqrt{(a - 0)^2 + (b - 0)^2 + (c - c)^2}$ $d = \sqrt{a^2 + b^2 + 0^2}$ $d = \sqrt{a^2 + b^2}$ Thus,the distance is $\sqrt{a^2 + b^2}$.

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

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