The equation of the plane which is parallel to 2x − 3y + z = 0 and which passes through (1, −1, 2) is:

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2x − 3y + z − 7 = 0 Explanation: Given, 2x − 3y + z = 0 ......(i) Equation of plane parallel to (i) is, 2x − 3y + z = d ...........(ii) Which is passes through (1, −1, 2), then 2 $\times$ 1 − 3 $\times$ (− 1) + 2 = d $\Rightarrow$ d = 7 Now from (ii), we get 2x − 3y + z = 7 or 2x − 3y + z − 7 = 0

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