Answer:
it is up
Step-by-step explanation:
Answer:
6x + 3y
Step-by-step explanation:
Multiply 3 by 2x.
Multiply 3 by y.
This is known as the distributive law.
The cross product of two vectors gives a third vector
![\mathbf v](https://tex.z-dn.net/?f=%5Cmathbf%20v)
that is orthogonal to the first two.
![\mathbf v=(\vec i+\vec j+\vec k)\times(4\,\vec i+\vec k)=\begin{vmatrix}\vec i&\vec j&\vec k\\1&1&1\\4&0&1\end{vmatrix}=\vec i+3\,\vec j-4\,\vec k](https://tex.z-dn.net/?f=%5Cmathbf%20v%3D%28%5Cvec%20i%2B%5Cvec%20j%2B%5Cvec%20k%29%5Ctimes%284%5C%2C%5Cvec%20i%2B%5Cvec%20k%29%3D%5Cbegin%7Bvmatrix%7D%5Cvec%20i%26%5Cvec%20j%26%5Cvec%20k%5C%5C1%261%261%5C%5C4%260%261%5Cend%7Bvmatrix%7D%3D%5Cvec%20i%2B3%5C%2C%5Cvec%20j-4%5C%2C%5Cvec%20k)
Normalize this vector by dividing it by its norm:
![\dfrac{\mathbf v}{\|\mathbf v\|}=\dfrac{\vec i+3\,\vec j-4\,\vec k}{\sqrt{1^2+3^2+(-4)^2}}=\dfrac1{\sqrt{26}}(\vec i+3\,\vec j-4\vec k)](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cmathbf%20v%7D%7B%5C%7C%5Cmathbf%20v%5C%7C%7D%3D%5Cdfrac%7B%5Cvec%20i%2B3%5C%2C%5Cvec%20j-4%5C%2C%5Cvec%20k%7D%7B%5Csqrt%7B1%5E2%2B3%5E2%2B%28-4%29%5E2%7D%7D%3D%5Cdfrac1%7B%5Csqrt%7B26%7D%7D%28%5Cvec%20i%2B3%5C%2C%5Cvec%20j-4%5Cvec%20k%29)
To get another vector orthogonal to the first two, you can just change the sign and use
![-\mathbf v](https://tex.z-dn.net/?f=-%5Cmathbf%20v)
.
First let's get rid of the parenthesis:
12 - 4x + 3x = 4 + 10 + 2x
Now group the x's on the left and the numbers on the right
-4x + 3x - 2x = 4 + 10 - 12
...and simplify
-3x = 2
divide by -3 to isolate x
x = -2/3
Answer:
2.5
Step-by-step explanation:
when you 5x automatically cancels, and 7.5 / 3 is 2.5