If the origin is shifted to $(1, 2, - 3)$ without changing the direction of the axes, then find the new coordinates of the point $(0, 4, 5)$ with respect to new frame.

(- 1, 2, 8)

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(0, 2, 3)

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(2, 3, - 1)

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None of these

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Solution

The correct option is B $(- 1, 2, 8)$
$x^{'} = x - x_{1} \Rightarrow x^{'} = 0 - 1 = - 1$
$y^{'} = y - y_{1} \Rightarrow y^{'} = 4 - 2 = 2$
$z^{'} = z - z_{1} \Rightarrow z^{'} = 5 + 3 = 8$
where $(x_{1}, y_{1}, z_{1})$ is the shifted origin.
The co-ordinates of the point w.r.t to new co-ordinate from is $(- 1, 2, 8)$

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