Question

If l, m and n are direction cosines of the position vector OP the coordinates of P are
l, mr and nr
lr, mr and n
lr, mr and nr
lr, m and nr

Answer 1

c) lr , mr and nr is the ans

Answer 2

Concept :

We first need to recall the concept of direction cosines and direction ratios of a vector.

If l, m and n are direction cosines of  a vector , then $l^{2} +m^{2} +n^{2} =1.$

and x, y,z be three numbers such that  $\frac{l}{x} =\frac{m}{y} =\frac{n}{z}$, then direction ratios or direction numbers of vector r are proportional in x,y and z. where

r= x i +y j +z k.

Given:

l , m and n are direction cosines of position vector OP.

To find:

The coordinates of P.

Solution:

let the coordinates of P be (x,y,z) and coordinates of O be (0,0,0)

then OP = x i+ y j+ z k

              = r

direction cosines  of P are given  by:

l = x / $\sqrt{x^{2} +y^{2}+z^{2} }$ ,

m = y / $\sqrt{x^{2} +y^{2}+z^{2} }$

n = z / $\sqrt{x^{2} +y^{2}+z^{2} }$.

where $\sqrt{x^{2} +y^{2}+z^{2} }$ = |r|

Hence, coordinates of P are ( lr ,mr ,nr).

Option (C) is correct choice.