Give an equation for the plane a through the origin and p

Give an equation for the plane . . .

a) through the origin and perpendicular to the vector <1, ?2, 5>.

b) through (1, ?1, ?1) parallel to the plane 5x ? y ? z = 6.

Unless a problem says otherwise, your answer may be in vector, scalar, or standard form.

Please show the workings!

Point (x0,y0,z0) = (0,0,0)

Normal vector = <a,b,c> = <1 , -2 , 5>

So, equation of plane is :

a(x - x0) + b(y - y0) + c(z - z0) = 0

Plug in :

1(x - 0) - 2(y - 0) + 5(z - 0) = 0

x - 2y + 5z = 0 -----> ANSWER

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b) through (1, ?1, ?1) parallel to the plane 5x ? y ? z = 6.

x0,y0,z0 = (1 , -1 , -1)

a , b , c = <5 , -1 , -1>

5(x - 1) - 1(y + 1) - 1(z + 1) = 0

5x - 5 - y - 1 - z - 1 = 0

5x - y - z - 7 = 0

5x - y - z = 7 ---> ANSWER