Find the equation of the plane passing through the point (0, 7, -7) an

1.	Find the equation of the plane passing through the point (0, 7, -7) and containing the line (x + 1)/-3 = (y - 3)/2 = (z + 2)/1.
Answer» Any plane passing through (0, 7, -7) is a (x - 0) + b(y - 7) + c(z + 7) = 0 ...(i) If (i) contains the give line then it must pass through the point (-1, 3, -2) and must be parallel to the given line. If (i) passes through (-1, 3, -2) then a(-1 - 0) + b(3 - 7) + c(-2 + 7) = 0 a + 4b - 5c = 0 ...(ii) If (i) is parallel to the given line then, (-3)a + 2b + 1.c = 0 -3a + 2b + c = 0 ...(iii) By cross multiplication of (ii) and (iii) we get a/(4 + 10) = b/(15 - 1) = c/(2 + 12) a/14 = b/14 = c/14 a/1 = b/1 = c/1 = k a = k, b = k, c = k Putting a = k, b = k and c = k in (i), we get the required equation of the plane as k(x - 1) + k(y - 7) + k(z - 7) = 0 x + (y - 7) + (z + 7) = 0 x + y + z = 0

Find the equation of the plane passing through the point (0, 7, -7) and containing the line (x + 1)/-3 = (y - 3)/2 = (z + 2)/1.

Answer»

Any plane passing through (0, 7, -7) is a (x - 0) + b(y - 7) + c(z + 7) = 0 ...(i)

If (i) contains the give line then it must pass through the point (-1, 3, -2) and must be parallel to the given line.

If (i) passes through (-1, 3, -2) then

a(-1 - 0) + b(3 - 7) + c(-2 + 7) = 0

a + 4b - 5c = 0 ...(ii)

If (i) is parallel to the given line then, (-3)a + 2b + 1.c = 0

-3a + 2b + c = 0 ...(iii)

By cross multiplication of (ii) and (iii)

we get a/(4 + 10) = b/(15 - 1) = c/(2 + 12)

a/14 = b/14 = c/14

a/1 = b/1 = c/1 = k

a = k, b = k, c = k

Putting a = k, b = k and c = k in (i), we get the required equation of the plane as k(x - 1) + k(y - 7) + k(z - 7) = 0

x + (y - 7) + (z + 7) = 0

x + y + z = 0

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