The coordinates of the point P are (x, y, z) | vedclass

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(C) Let the point $P$ be $(x, y, z)$ and the origin $O$ be $(0, 0, 0)$.The distance $r$ of the point $P$ from the origin is given by $r = \sqrt{x^2 +

Vedclass · Accepted Answer

$x = lr, y = mr, z = nr$

Vedclass · Answer

(C) Let the point $P$ be $(x, y, z)$ and the origin $O$ be $(0, 0, 0)$.The distance $r$ of the point $P$ from the origin is given by $r = \sqrt{x^2 + y^2 + z^2}$.The direction cosines $l, m, n$ of the line $OP$ are defined as the cosines of the angles $\alpha, \beta, \gamma$ that the line makes with the $x, y, z$ axes respectively.By definition,$l = \cos \alpha = \frac{x}{r}$,$m = \cos \beta = \frac{y}{r}$,and $n = \cos \gamma = \frac{z}{r}$.Multiplying these expressions by $r$,we get $x = lr$,$y = mr$,and $z = nr$.Thus,the correct relation is $x = lr, y = mr, z = nr$.

The coordinates of the point $P$ are $(x, y, z)$ and the direction cosines of the line $OP$ where $O$ is the origin $(0, 0, 0)$ are $l, m, n$. If $r$ is the distance $OP$,then which of the following relations is correct?

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