Finding scalar equation of a line with a vector and a point given

[BlazeKH]

I would really appreciate the help, I've been trying to figure this out for the last three hours no joke.

Homework Statement

Write the scalar equation the line given the normal vector [3,1] and point (2,4)

Homework Equations

R=[X0,Y0]+ T[M1,M2]

The Attempt at a Solution

R=[2,4] + T[3,1]

X=2+3T Y=4+T

(X-2)/3=T Y-4=T

(X-2)/3=Y-4

X-2=3Y-12

X-3Y+10=0

ANSWER:3X+2Y-10

 

[rock.freak667]

You need to find the vector parallel to the line you want i.e. the vector normal to the normal.

The dot product of the parallel line and the normal is zero. Use that to get the required parallel vector.

 

[BlazeKH]

I tried that but it didn't work, am I doing something wrong?

[X,Y].[3,1]=0

3X+Y=0

Y=-3X (I subbed in a point, to my understanding it shouldn't matter which)

Y=-3(1)

Y=-3

P=[1,-3]

R=[2,4]+T[1,-3]

X=2+T Y=4-3T

X-2=T (Y-4)/-3=T

-3X+6=Y-4

-3X-Y+10=0

 

[BlazeKH]

Okay I figured it out the answer is also incorrect btw.