Question

If O is the origin and OP = 6 with direction ratios proportional to –1, 2, –2 then the coordinates of P are _____________.

Answer 1

Let us suppose co-ordinate of P are (a, b, c)
Now, since direction ratios are proportional to –1, 2, –2.
$\therefore \frac{a}{-1}=\frac{b}{2}=\frac{c}{-2}=\lambda$
i.e a = –λ, b = 2λ, c = –2λ
Since OP = 6

$\therefore \sqrt{{\left(-\lambda -0\right)}^2+{\left(2\lambda -0\right)}^2+{\left(-2\lambda -0\right)}^2}=6$

i.e λ² + 4λ² + 4λ² = 36
i.e 9λ² = 36
i.e λ = ±2 ∴ Co-ordinates of P are ( –2, 4, –4)