Find parametric equations of the line perpendicular to the lines l1: x = 1 − t, y = t, z = 5t − 4 and l2: x = t + 1, y = −t, z = t − 4 at their point of intersection. (enter your answers as a comma-separated list of equations.) why is this line parallel to the xy-plane? this line is parallel to the xy-plane because its is constant.

Q : X = 6λ+1,Y=6λ,Z=-4 ; λ∈R

This line is parallel to the X-Y plane because in its ''Z'' component the number that multiplies to the parameter λ is 0.

Step-by-step explanation:

First we are going to find the intersection between l1 and l2.

X=X , Y=Y , Z=Z that is how we find the intersection

1-t=t+1 (1)

t=-t (2)

5t-4=t-4 (3)

From equation (2) t=0 (We must verify this in (1) and (2))

Replacing t=0 in l1 or in l2 we find that the intersection is I=(1,0,-4)

To find the direction of the line Q we need to calculate the vector product of the directions of l1 and l2

The direction of l1 is (-1,1,5) and from l2 is (1,-1,1)

The direction is given by the numbers that multiplies the t variable in the equations

(-1,1,5) X (1,-1,1) = (6,6,0)

Notice that (-1,1,5).(6,6,0) = 0 so Q will be perpendicular to l1 and (1,-1,1).(6,6,0)=0 so Q will be perpendicular to l2

We have got the direction from Q and a point that belongs to Q so we can write the equations

Q:(X,Y,Z) = λ(6,6,0)+(1,0,-4) ; λ∈R this is the vectorial equation of Q

To find the parametric equation we need to do the following

(6λ,6λ,0)+(1,0,-4) = (6λ+1,6λ,-4)=(X,Y,Z)

Q : X = 6λ+1,Y=6λ,Z=-4 ; λ∈R

Q//X-Y plane because of its ''Z'' component direction that its equal to 0.

answer: the answer is (b) amie should have multiplied

step-by-step explanation: given a sphere and a cylinder with same radius and height.

let, 'r' be the radius of the cylinder and sphere and 'h' be the height of the cylinder. according to the question,

r = h.

now, the volume of the sphere will be

and the volume of the cylinder will be

therefore, we have

thus, ammie should have multiplied the volume of the sphere

she was supposed to add the hours(38.5) and multiply the amount of money she earned(7.50) resulting in $288.75 .

correct me if i'm wrong and if it is i'm truly sorry.