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The vector equation of the plane passing through the points (1,–2,5),(0,–5,–1),(–3,5,0) is

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$[r - (i - 2 j + 5 k), - i - 3 j - 6 k, - 4 i + 7 j - 5 k] = 0$

$[r - 5 j - k, - 3 i + 5 j] = 0$

$[r, - i - 3 j - 6 k, - 4 i + 7 j - 5 k] = 0$

$[r - (i - 2 j + 5 k), - 5 j - k, - 3 i + 5 j] = 0$

answer is C.

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Detailed Solution

$\begin{array}{rcl} [AB AC AD] & = & 0 \end{array}$

$\begin{array}{rcl} [r - (i - 2 j + 5 k), - i - 3 j - 6 k, - 4 i + 7 j - 5 k] & = & 0 \end{array}$

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