The cross product of the normal vectors of two planes result in a vector parallel to the line of intersection of the two planes.
Corresponding normal vectors of the planes are
<5,-1,-6> and <1,1,1>
We calculate the cross product as a determinant of (i,j,k) and the normal products
i j k
5 -1 -6
1 1 1
=(-1*1-(-6)*1)i -(5*1-(-6)1)j+(5*1-(-1*1))k
=5i-11j+6k
=<5,-11,6>
Check orthogonality with normal vectors using scalar products
(should equal zero if orthogonal)
<5,-11,6>.<5,-1,-6>=25+11-36=0
<5,-11,6>.<1,1,1>=5-11+6=0
Therefore <5,-11,6> is a vector parallel to the line of intersection of the two given planes.
<h2>Equations of Circles</h2>
Generally, you'd see the equation of a circle organized in the following format:
is the center
is the radius
To determine the equation given the center and the radius:
- Plug both pieces of information into the general equation
- Simplify
<h2>Solving the Question</h2>
We're given:
- Radius: 99
- Center: (-1,-8)
Plug the radius and center into the equation as r and (h,k):
<h2>Answer</h2>
Answer:
Step-by-step explanation:
approximately 0.94625 liters per second
Any graph is defined by a given function. A graph of x +y =3, may be described as a line joining points such the sum of x-coordinate and the y-coordinate is 3. These are points such as (1,2), (2,1), (3,0) and so on such that the satisfy the equation of the line.
