Find the line through (8, 1, −5) that intersects and is perpendicular to the line x = −1 + t, y = −3 + t, z = −1 + t. (hint: if (x0, y0, z0) is the point of intersection, find its coordinates. enter your answers as a comma-separated list of equations.)

Step-by-step explanation:

A line passing through the point (8, 1, −5) and perpendicular to the line x = −1 + t, y = −3 + t, z = −1 + t.

The parallel vector of given line is < 1, 1, 1 >.

Let the point of intersection is  (-1+t, -3+t, -1+t).

The required line passing through the points (8, 1, −5) and  (-1+t, -3+t, -1+t). So, the vector of required line is

< 8-(-1+t), 1-(-3+t), -5-(-1+t) >

< 9-t, 4-t, -4-t >

The dot product of two perpendicular vectors is 0.

Since < 9-t, 4-t, -4-t > and < 1, 1, 1 > are perpendicular vectors, therefore the dot product of these vectors is 0.

The value of t is 3. So, the point of intersection is

If a line passes through two points then the equation of line is

The line passes through two points (8, 1, −5) and (2,0,2). So, the equation of line is

Let

Therefore the parametric equations of the required line are .

30 people weigh 160 pounds or more

step-by-step explanation: so we look at the formula un = a + (n-1)d

un is the amount of seats

n is the nth term aka row number

a is the original sequence/row number

d is the difference between each term

so in this a=22 d=6 and n can remain as n because we are simply formjng a rule

lets put these in the equation

un=22+(n-1)(6)

this is your answer to part a

however

lets double check that this is correct, we'll try putting it into the second term

un=a+(n-1)d

u2=22+(2-1)(6)

u2=22+6

u2=28

as the question said the second row has 28 seats so now we know the formula we made is correct.

as for part b

un=a+(n-1)

its asking us to find a row with 100 seats.

remember un was the amount of seata so all we do is substitute this in.

un=100 a=22 d=6

un=a+(n-1)d

100=22+(n-1)(6)

so now we simplify to find n which is the row number.

100-22=22+(n-1)(6)-22

78=(n-1)(6)

78/6=(n-1)(6)/6

13=n-1

13+1=n-1+1

14=n

so now we know that in the 14th row there is 100 seats.

hope this and that you understood! its my first time using the app or anyone out on here : p its also me to revise so a bunch! ask more questions if you dont understand ☺