Law of cosines - vector, Mathematics

Assignment Help:

Theorem

a • b = ||a|| ||b|| cos•

Proof

Let us give a modified version of the diagram above.

1804_Law of Cosines - vector 1.png

The three vectors above make the triangle AOB and note that the length of each side is nothing much more than the magnitude of the vector forming that side.

 The Law of Cosines defines that,

||a- b||2 = ||a||2 + ||b||2 - 2 ||a|| || b|| cos•

As well by using the properties of dot products we can write the left side as,

||a- b||2 = (a - b) • (a - b)

= a• a - a•b - b•a + b• b

= || a||2 - 2a • b + || b||2

After that our original equation is,

1565_Law of Cosines - vector.png


Related Discussions:- Law of cosines - vector

Quadric surfaces - three dimensional spaces, Quadric Surfaces Earlier w...

Quadric Surfaces Earlier we have looked at lines and planes in three dimensions (or R 3 ) and when these are used fairly heavily at times in a Calculus class there are several

Introduction to mathematics, We know that one has to deal with ...

We know that one has to deal with numbers in day-to-day life irrespective of his inclination and field of work. Also one cannot refute the fact

Angles, samuel left mauritius at 22:30 on saturday and travelled to london ...

samuel left mauritius at 22:30 on saturday and travelled to london (GMT) for 14h30min he had a stopover for 4 h in london and he continued to travel to toronto for another 6h20min

Diferential equations, Find the normalized differential equation which has ...

Find the normalized differential equation which has {x, xex} as its fundamental set

Example of division , Example of division: Divide 738 by 83. Soluti...

Example of division: Divide 738 by 83. Solution: Example: Divide 6409 by 28. Solution: Division could be verified through multiplying

Linear functions, Linear functions are of the form: y = a 0 ...

Linear functions are of the form: y = a 0 + a 1 x 1 + a 2 x 2 + ..... + a n x n where a 0 , a 1 , a 2 ..... a n are constants and x 1 , x 2 ..... x n a

Example of developing an understanding, I gave my niece a whole heap of bea...

I gave my niece a whole heap of beads and showed her how to divide it up into sets of 10 beads each. Then I showed her how she could lay out each set of I0 beads in a line, and cal

Find sampling interval - horizontal and vertical asymptote, In a digital fi...

In a digital filter, one of the parameters in its difference equation is given by the formula a) Show that the above formula has one horizontal and one vertical asymptote.

Stats, the automatic hopper loader is set to put 36 tons of coal in each ca...

the automatic hopper loader is set to put 36 tons of coal in each car. the actual weights of coal loaded into each car arw normally distributed with a mean of 36 tons and a standar

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd