Question

The direction ratios of the line OP are equal and the length $OP = \sqrt{3}$ . Then the coordinates of the point P are :

• A. ( -1, - 1, -1)
• B. $( \sqrt{3} , \sqrt{3} , \sqrt{3})$
• C. $( \sqrt{2} , \sqrt{2} , \sqrt{2})$
• D. (2, 2, 2)

Answer 1

Answer: (A)

( -1, - 1, -1)

Answer 2

Let coordinates of P be (x, y, z), O is origin. Direction ratios of OP are, a = 0 - x b= 0 - y c = 0 - z $\Rightarrow$ As given: a, b, c are equal $\Rightarrow$ x = y = z $\Rightarrow$ OP = $\sqrt{(0 -x)^2 + (0 - y)^2 + (0 -z)^2} = \sqrt{3}$ $[ \because \, OP = \sqrt{3} ]$ $\Rightarrow \, \sqrt{3x^2} = \sqrt{3} \, \Rightarrow 3x^2 = 3$ $\Rightarrow \, x^2 = 1$ $\Rightarrow x = \pm 1$ $\Rightarrow x = - 1, y = - 1, z = -1$ or $x = 1, y = 1, z =1$ $\therefore$ Coordinates of P = (- 1, - 1, - 1) is given in the choice.