Mathematics, 15.01.2020 22:31, machucagm01

Find a set of parametric equations for the line of intersection of the planes x-3y+6z=4 5x+y-z=4

Answers: 2

Show answers

Answers

answered: floresguppy

Step-by-step explanation:

Two equations of planes are given.

We have to find the equation of the line which is formed by intersection of these two planes in parametric form

$x-3y+6z=4 \\5x+y-z=4$

Let us eliminate one variable

Multiply I equation by 5 and subtract II from 5 * I

$5x-15y+30z=20 \\5x+y-z=4$

$-16y+31z=16 \\$

16y+16 = 31z

Or $y+1 =\frac{31z}{16}$

Consider II equation

5x+y-z=4

$5x+\frac{31z}{16}-1 -z=4\\5x+\frac{15z}{16}=5\\x=\frac{3z-16}{16}$

Let z=z

x = \frac{3z-16}{16} and y = \frac{31z}{16}-1

answered: pinklavalamp

Parametric equation of line of intersections of the planes.

x(t) = 1 - 3t

y(t) = 31t - 1

z(t) = 16t

Explanation:

The equation of planes are x-3y+6z=4 and 5x+y-z=4

Equation of first plane: x-3y+6z=4Normal vector of this plane, n_1=

Equation of 2nd plane: 5x+y-z=4Normal vector of this plane, n_1=

Point of intersection of x-3y+6z=4 and 5x+y-z=4

Let z = 0

x - 3y = 4 and 5x + y = 4

solve for x and y

x = 1 and y = -1

Point of intersection of plane, (1,-1,0)

The line of intersection of both plane must be passes through this point.

Parallel vector of line is cross product of $n_1\times n_2$

$\bec{b}=\times$

$\vec{b}=$

Equation of line:-

$\dfrac{x-1}{-3}=\dfrac{y+1}{31}=\dfrac{z-0}{16}=t$

Parametric equation of line:-

x(t) = 1 - 3t

y(t) = 31t - 1

z(t) = 16t

answered: Guest

step-by-step explanation:

it have 5 sides and 5 identicle angle.the rest does not have the same property as b.

brainliest

answered: Guest

the population of other specie of birds will decline or other specie of birds will find some alternate source of food to survive.

explanation:

according to the competitive exclusion principle, which is also known as gause's law, two specie living in the same niche and feeding on the same resource cannot co-exist stably.

as we have well studied the theory of natural selection which states that only those organisms survive which have better tendency to compete for food and adapt to the environmental conditions.

coming towards the question, what wi ll happen when one species outcompetes the other for the small fish , the other specie will not get enough food and will start to die or decline in population. eventually either other specie needs to find another alternative food source for itself or migrate at some other location where there is less competition otherwise it will just not exist anymore at that niche.

hope it !