Find conditions on a; b; c; d that ensures that the plane pi : ax + by + cz = d is perpendicular to the plane 4x - 2y + z = 3.

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sciencesolve | Teacher | (Level 3) Educator Emeritus

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You need to remember that two plane are perpendicular to each other if the normal vectors to the planes are also perpendicular to each other, hence, you need first to determine the normal vectors to the planes, such that:

bar n_1 = <a,b,c>

`bar n_2 = <4,-2,1>`

You need to remember that two vectors are perpendicular to ecah other if evaluating the dot product yields 0, such that:

`bar n_1*bar n_2 = 0 <=><a,b,c>*<4,-2,1> = 0`

`<a,b,c>*<4,-2,1> = 4a - 2b + c =>4a - 2b + c = 0`

Hence, evaluating the relation between `a,b,c` for the planes to be perpendicular, yields `4a - 2b + c = 0.`

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