the answer is 2
there are 13 days, 6x2=12. so the answer is 2.
![\vec r(t)=\langle6t,1+3t,4t\rangle](https://tex.z-dn.net/?f=%5Cvec%20r%28t%29%3D%5Clangle6t%2C1%2B3t%2C4t%5Crangle)
![\vec R(s)=\langle2+s,-8+3s,-12+4s\rangle](https://tex.z-dn.net/?f=%5Cvec%20R%28s%29%3D%5Clangle2%2Bs%2C-8%2B3s%2C-12%2B4s%5Crangle)
Take the derivatives of each to get the tangent vectors:
![\dfrac{\mathrm d\vec r(t)}{\mathrm dt}=\langle6,3,4\rangle](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cmathrm%20d%5Cvec%20r%28t%29%7D%7B%5Cmathrm%20dt%7D%3D%5Clangle6%2C3%2C4%5Crangle)
![\dfrac{\mathrm d\vec R(s)}{\mathrm ds}=\langle1,3,4\rangle](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cmathrm%20d%5Cvec%20R%28s%29%7D%7B%5Cmathrm%20ds%7D%3D%5Clangle1%2C3%2C4%5Crangle)
Take the cross product of the tangent vectors to get a vector that is normal to both lines:
![\langle6,3,4\rangle\times\langle1,3,4\rangle=\langle0,-20,15\rangle](https://tex.z-dn.net/?f=%5Clangle6%2C3%2C4%5Crangle%5Ctimes%5Clangle1%2C3%2C4%5Crangle%3D%5Clangle0%2C-20%2C15%5Crangle)
The two given lines intersect when
:
![\langle6t,1+3t,4t\rangle=\langle2+s,-8+3s,-12+4s\rangle\implies t=1,s=4](https://tex.z-dn.net/?f=%5Clangle6t%2C1%2B3t%2C4t%5Crangle%3D%5Clangle2%2Bs%2C-8%2B3s%2C-12%2B4s%5Crangle%5Cimplies%20t%3D1%2Cs%3D4)
that is, at the point (6, 4, 4).
The line perpendicular to both of the given lines through the origin is obtained by scaling the normal vector found earlier by
; translate this line by adding the vector
to get the line we want,
![\vec\rho(\tau)=\langle6,4,4\rangle+\langle0,-20,15\rangle\tau](https://tex.z-dn.net/?f=%5Cvec%5Crho%28%5Ctau%29%3D%5Clangle6%2C4%2C4%5Crangle%2B%5Clangle0%2C-20%2C15%5Crangle%5Ctau)
![\boxed{\vec\rho(\tau)=\langle6,4-20\tau,4+15\tau\rangle}](https://tex.z-dn.net/?f=%5Cboxed%7B%5Cvec%5Crho%28%5Ctau%29%3D%5Clangle6%2C4-20%5Ctau%2C4%2B15%5Ctau%5Crangle%7D)
Answer:
your
Step-by-step explanation:
Answer:
I got 45
Step-by-step explanation:
so I did the triangle first I did 5 times 6 divided by 2 and got 15 then I did 5 times 6 and got 30 then I added the 30 and 15 together.
The answer is A confirming appointments for the director of the facility