Find an equation of the plane. the plane through the point (−5, 9, 10) and perpendicular to the line x = 1 + t, y = 4t, z = 2 − 3t

The equation of the plane will be

First and foremost, since we are given the information that the plane passes through the point and is then perpendicular to the line x =  

Based on the above information, the direction vector of the line will be 1, 4, -3 which are the coefficients of t.

Since the plane goes through point , therefore the required plane will be:

Then, we'll solve this equation which will be:

Collect like terms

Therefore, the equation of the plane will be

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