If OP-21 and d-c-s of OP are 27-67- - 37- then find the co-ordinates of P-

Consider the coordinates of P be (x,y,z) then, l=xOP 27=x21 x=6 m=yOP 67=yOP y=18 n=zOP 37=z21 z= 9 Ther ...

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Byju's Answer

Standard VII

Mathematics

Pythagoras Theorem

If OP=21 and ...

Question

If OP=21 and d.c.'s of $- - \to O P$ are $(\frac{2}{7}, \frac{6}{7}, - \frac{3}{7})$ , then find the co-ordinates of P.

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Solution

consider the coordinates of $P$ be $(x, y, z)$
then,
$l = \frac{x}{O P}$

$\frac{2}{7} = \frac{x}{21}$

$x = 6$

$m = \frac{y}{O P}$

$\frac{6}{7} = \frac{y}{O P}$

$y = 18$

$n = \frac{z}{O P}$

$\frac{- 3}{7} = \frac{z}{21}$

$z = - 9$

Therefore,
Coordinates of point $P$ are $(6, 18, - 9)$

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Assertion ( $A$ ): lf the direction ratios of a line are $(- 6, 2, 3)$ then the angles made by the line with coordinate axes are ${cos}^{- 1} (\frac{- 6}{7}), {cos}^{- 1} (\frac{2}{7}), {cos}^{- 1} (\frac{3}{7})$ .

Reason $(R)$ : The $d . c$ 's of a line $¯ ¯¯¯¯¯¯ ¯ O P$ are $(\frac{x}{r}, \frac{y}{r}, \frac{z}{r})$ , where $| ¯ ¯¯¯¯¯¯ ¯ O P | = r$ and $p = (x, y, z)$ .