The line
runs in the direction of its tangent vector; we can get it by taking its derivative:
![\vec T=\dfrac{\mathrm d}{\mathrm dt}\left[(11,-8,4)+t(3,-1,1)\right]=(3,-1,1)](https://tex.z-dn.net/?f=%5Cvec%20T%3D%5Cdfrac%7B%5Cmathrm%20d%7D%7B%5Cmathrm%20dt%7D%5Cleft%5B%2811%2C-8%2C4%29%2Bt%283%2C-1%2C1%29%5Cright%5D%3D%283%2C-1%2C1%29)
Any line that runs perpendicular to this line will have a tangent vector that is orthogonal to 
above. So construct some vector 
that satisfies this.
Suppose 
; then 
, and we can pick any two values that satisfy this condition. For instance,
And of course,
(1, 3, 0) • (3, -1, 1) = 3 - 3 + 0 = 0
so and are indeed orthogonal.
Now, the line running in the direction of and passing through the origin can be obtained by scaling
More generally, if you have a direction/tangent vector and some point 
, the line through is given by
Answer: 120
Step-by-step explanation:
The permutation of n things taken r at a time is given by expression :-
The formula to evaluate is given by :-
Then , 
will be :-
Since , 
Then , 
Therefore, the value of the expression 
Answer:
10.8 meters
Step-by-step explanation:
1.2 times 9 minutes= 10.8
The answer is D, i.e. the system was solved via elimination
If you multiply the first equation by 5, the system becomes
If you sum the two equations, you get
And so if you substitute the second equation of system A with this new equation, you'll get system B.
Answer:
Step-by-step explanation:
