- #1

Physics345

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## Homework Statement

Find the scalar, vector, and parametric equations of a plane

that has a normal vector n→=(3,−4,6) and passes through the point P(9, 2, –5).

## Homework Equations

Ax+By+Cz+D=0

(x,y,z)=(x0,y0,z0)+s(a1,a2,a3)+t(b1,b2,b3)

x=x0+sa1+tb1

y=y0+sa2+tb2

z=z0+sa3+tb3

## The Attempt at a Solution

Scalar Equation:

3x-4y+6z+D=0

3(9)-4(2)+6(-5)+D=0

D=11

3x- 4y +6z+11=0

Vector Equation:

4y=3x+6z+11

y=3/4 x+6/4 z+11

y=3/4 x+3/2 z+11

P(9,2,-5)

Let x=0 and z=0

y=11

Q(0,11,0)

let x=2 and z=1

y=3/4(2)+3/2(1)+11

y=14

R(2,14,1)

(PQ) ⃗ =Q-P

(PQ) ⃗ =(0,11,0)-(9,2,-5)=(-9,9,5)

(PR) ⃗ =R-P

(PR) ⃗ =(2,14,1)-(9,2,-5)=(-7,12,6)

(x,y,z)=(9,2,-5)+s(-9,9,5)+t(-7,12,6)

Parametric Equations:

x=9-9s-7t

y=2+9s+12t

z=-5+5s+6t

Did I do this correctly? And is there anyway to confirm my answers through math? Thanks in advance =)