Discrete Math: Equations of Line in a Plane
posted by Anonymous .
I'm stuck on these questions. Can you please show me a step by step solution?
20) For each of the following, find a normal vector, a direction vector, and a point of each line.
Note, normal vector means perpendicular to the direction vector.
a) 3x  6y = 14
TEXTBOOK ANSWER:
normal vector = (1 , 2)
direction vector = (2 , 1)
point on the line = [(14/3) , 0]

21) Find vector, parametric, and symmetric equations of the following lines.
a) 4x + 6y + 9 = 0
TEXTBOOK ANSWER:
Vector Equation > r = [0 , (3/2)] + t(3 , 2)
Parametric Equation > x = 3t and y = 2t  (3/2)
Symmetric Equation > (x/3) = [y + (3/2)] / 2

I will do the second one, since it looks a bit more difficult than the first
You are clearly working in only 2D here.
I assume you know that for any straight line
Ax + By + C = 0
[A,B] is a normal to the line which makes
[B,A] a direction vector
and the slope of the line is A/B
the vector equation of a line in 2D is
r = [any point on the line] + t[direction vector of the line], where t is a parameter.
so they started by letting x=0, then y = 9/6 = 3/2
so the point they used is (0,3/2)
and the direction of the line is [6,4] or [3,2]
so the vector equation is
r = [0,3/2] + t[3,2] as shown in your text.
if we "expand" that we get
r = [0+3t,3/2 + 2t]
from that you can see that the
x=3t and the
y=3/2 + 2t as shown in your book answer
now if we solve these last two equations for t we get
t = x/3 and t = (y+3/2)/2
equating t=t gives us their third answer of
x/3 = (y+3/2)/2
Respond to this Question
Similar Questions

physics
A roller coaster moves 85 m horizontally, then travels 45 m at an angle of 30.0 degrees above the horizontal. What is its displacement from its starting point? 
Physics/Math
In the vector sum A + B = C , vector A has a magnitude of 13.1 m and is angled 49° counterclockwise from the +x direction, and vector C has a magnitude of 15.0 m and is angled 20.0° counterclockwise from the x direction. What are … 
Math: Equations of Line in a Plane
I'm stuck on these questions. Can you please show me a step by step solution? 
Pre Calc
find the magnitude and direction angle of the vector v, v=2i+5j please help i have no idea how to do this. could you show me step by step? 
Math  Equations of plane(check)
Consider the plane that contains points A(2,3,1), B(11,1,2), C(7,3,6). a) Find two vectors that are parallel to the plane. Ans: AC, BC or AB will be parallel to the plane. b) Find two vectors that are perpendicular to the plane. … 
Math  Equations of plane(check)
Consider the plane that contains points A(2,3,1), B(11,1,2), C(7,3,6). a) Find two vectors that are parallel to the plane. Ans: AC, BC or AB will be parallel to the plane. b) Find two vectors that are perpendicular to the plane. … 
Precalc
A line in space has the vector equation shown here. Fill in the blanks to find the position vector to the fixed point on the line that appears in the equation: vector r=(5+(6/11)d)vector i + (3+(9/11)d)vector j + (7+(2/11)d)vector … 
Precalc
Given the plane 3x+2y+5z=54 and the points P0(6, 8, 4)[on plane] and P1(13, 18, 5) [not on plane] A. Find vector n, a vector normal to the plane B. Find vector v from P0 to P1 C. Find the angle between vector n and vector v D. Find … 
Physics
You are given vectors A = 5.0i  6.5j and B = 2.5i + 7.0j. A third vector C lies in the xyplane. Vector C is perpendicular to vector A and the scalar product of C with B is 15.0. Find the x and y components to vector C. Here's the … 
calculus
State whether or not the following statements are true. Justify your reasoning.?