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# Solution for 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) - CBSE (Commerce) Class 12 - Mathematics

ConceptDirection Cosines and Direction Ratios of a Line

#### Question

If O is the origin, OP = 3 with direction ratios proportional to −1, 2, −2 then the coordinates of P are

•  (−1, 2, −2)

•  (1, 2, 2)

•  (−1/9, 2/9, −2/9)

•  (3, 6, −9)

#### Solution

(a) (1, 2,2)

Let the coordinates of P be (x, y, z). Then,

Direction ratios of OP= Coordinates of P Coordinates of O

1, 2, 2 = (x0), (y0), (z0)

Thus, coordinates of P are (1, 2,2).

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Solution 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) Concept: Direction Cosines and Direction Ratios of a Line.
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