Answer:
So the way to express a vector(
) as a product of its length and direction is
![v = |v| u = \sqrt{12} (\frac{2}{ \sqrt{12} } , -\frac{2}{ \sqrt{12} }, - \frac{2}{ \sqrt{12} })](https://tex.z-dn.net/?f=v%20%20%3D%20%20%20%20%7Cv%7C%20u%20%3D%20%20%5Csqrt%7B12%7D%20%28%5Cfrac%7B2%7D%7B%20%5Csqrt%7B12%7D%20%7D%20%2C%20-%5Cfrac%7B2%7D%7B%20%5Csqrt%7B12%7D%20%7D%2C%20-%20%5Cfrac%7B2%7D%7B%20%5Csqrt%7B12%7D%20%7D%29)
Step-by-step explanation:
Generally a vector is expressed as a product of its length and direction using the formula below
![v = |v|\cdot u](https://tex.z-dn.net/?f=v%20%20%3D%20%20%7Cv%7C%5Ccdot%20u)
Here v is the vector
|v| is its magnitude (length)
u is its unit vector (direction)
Now let take an example
Let
![v = 2i - 2j - 2k](https://tex.z-dn.net/?f=v%20%3D%20%202i%20-%202j%20-%202k)
The magnitude is mathematically evaluated as
![|v| = \sqrt{ 2^2 + (-2)^2 + (-2)^2 }](https://tex.z-dn.net/?f=%7Cv%7C%20%3D%20%20%5Csqrt%7B%202%5E2%20%20%2B%20%28-2%29%5E2%20%2B%20%20%28-2%29%5E2%20%7D)
![|v| = \sqrt{12}](https://tex.z-dn.net/?f=%7Cv%7C%20%3D%20%20%5Csqrt%7B12%7D)
The unit vector is mathematically represented as
![u = \frac{v}{|v|}](https://tex.z-dn.net/?f=u%20%20%3D%20%20%5Cfrac%7Bv%7D%7B%7Cv%7C%7D)
![u = \frac{ }{\sqrt{12} }](https://tex.z-dn.net/?f=u%20%20%3D%20%20%5Cfrac%7B%20%3C2%20%2C%20-2%20%2C%20-2%3E%7D%7B%5Csqrt%7B12%7D%20%7D)
![u = \frac{2}{ \sqrt{12} } , -\frac{2}{ \sqrt{12} }, - \frac{2}{ \sqrt{12} }](https://tex.z-dn.net/?f=u%20%3D%20%20%5Cfrac%7B2%7D%7B%20%5Csqrt%7B12%7D%20%7D%20%2C%20-%5Cfrac%7B2%7D%7B%20%5Csqrt%7B12%7D%20%7D%2C%20-%20%5Cfrac%7B2%7D%7B%20%5Csqrt%7B12%7D%20%7D)
So
![v = |v| u = \sqrt{12} (\frac{2}{ \sqrt{12} } , -\frac{2}{ \sqrt{12} }, - \frac{2}{ \sqrt{12} })](https://tex.z-dn.net/?f=v%20%20%3D%20%20%20%20%7Cv%7C%20u%20%3D%20%20%5Csqrt%7B12%7D%20%28%5Cfrac%7B2%7D%7B%20%5Csqrt%7B12%7D%20%7D%20%2C%20-%5Cfrac%7B2%7D%7B%20%5Csqrt%7B12%7D%20%7D%2C%20-%20%5Cfrac%7B2%7D%7B%20%5Csqrt%7B12%7D%20%7D%29)
Step-by-step explanation:
An important property of equations is one that states that you can add the same quantity to both sides of an equation and still maintain an equivalent equation. ... If you think of an equation as being like a balance scale, the quantities on each side of the equation are equal, or balanced.
Answer:
z = -2.5
Step-by-step explanation:
Subtract 9 on both sides to get this equation 2z=-5. Divide that number by 2 to get your final answer -2.5 as a result of z.
Answer:
-2,-3,-4.
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Answer:
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Step-by-step explanation: