The micrometre (International spelling as used by the International Bureau of Weights and Measures;[1] SI symbol: μm) or micrometer (American spelling), alsocommonly known as a micron, is an SI derived unit of length equaling 1×10−6 of ametre (SI standard prefix "micro-" = 10−6); that is, one millionth of a metre (or one thousandth of a millimetre, 0.001 mm, or about 0.000039 inch).[1] The symbol μm is sometimes rendered as um if the symbol μ cannot be used, or if the writer is not aware of the distinction.[citation needed]

The micrometre is a common unit of measurement for wavelengths of infrared radiation as well as sizes of biological cells and bacteria and is also commonly used in plastics manufacturing.[1] Micrometres are the standard for grading wool by the diameter of the fibres; wool finer than 25 μm can be used for garments, while coarser grades are used for outerwear, rugs, and carpets.[2] The width of a single human hair ranges from approximately 10 to 200 μm. The first and longest human chromosome is 10μm in length.

Contents [hide] 1Examples2SI standardization3Symbol4See also5Notes and references

4 0

3 years ago

Determine as a linear relation in x, y, z the plane given by the vector function F(u, v) = a + u b + v c when a = 2 i − 2 j + k,

Ostrovityanka [42]

Answer:

2x - y - 3z = 0

Step-by-step explanation:

Since the set

{i, j} = {(1,0), (0,1)}

is a base in $\mathbb{R}^2$

and F is linear, then

{F(1,0), F(0,1)}

would be a base of the plane generated by F.

F(1,0) = a+b = (2i-2j+k)+(i+2j+k) = 3i+2k

F(0,1) = a+c = (2i-2j+k)+(2i+j+2k) = 4i-j+3k

Now, we just have to find the equation of the plane that contains the vectors 3i+2k and 4i-j+3k

We need a normal vector which is the cross product of 3i+2k and 4i-j+3k

(3i+2k)X(4i-j+3k) = 2i-j-3k

The equation of the plane whose normal vector is 2i-j-3k and contains the point (3,0,2) (the end of the vector F(1,0)) is given by

2(x-3) -1(y-0) -3(z-2) = 0

or what is the same

2x - y - 3z = 0

3 0

3 years ago