Question

If O is the origin, OP = 3 with direction ratios proportional to −1, 2, −2 then the coordinates of P are
(a) (−1, 2, −2)
(b) (1, 2, 2)
(c) (−1/9, 2/9, −2/9)
(d) (3, 6, −9)

Answer 1

$$\begin{gathered} \left(\mathrm{a}\right)\left(-1,2,-2\right) \\ \mathrm{Let}\mathrm{the}\mathrm{coordinates}\mathrm{of}P\mathrm{be}\left(x\mathit{,}\mathit{}y\mathit{,}\mathit{}z\right).\mathrm{Then}, \\ \mathrm{Direction}\mathrm{ratios}\mathrm{of}OP=\mathrm{Coordinates}\mathrm{of}\mathit{}P-\mathrm{Coordinates}\mathrm{of}\mathit{}O \\ -1,2,2=\mathit{}\left(x\mathit{-}\mathit{0}\right)\mathit{,}\mathit{}\left(y\mathit{-}\mathit{0}\right)\mathit{,}\mathit{}\left(z\mathit{-}\mathit{0}\right) \\ \mathrm{Thus},\mathrm{coordinates}\mathrm{of}\mathrm{P}\mathrm{are}\left(\mathit{-}\mathit{1}\mathit{,}\mathit{}\mathit{2}\mathit{,}\mathit{-}\mathit{2}\right). \end{gathered}$$