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

Give a definition of perimeter and area, Give a Definition of Perimeter and...

Give a Definition of Perimeter and Area? Perimeter is the distance around a flat (2-dimensional) shape. Area is the amount of space taken up by a flat (2-dimensional) shape. is

Find the distance between these two cities, Memphis, Tennessee, and New Orl...

Memphis, Tennessee, and New Orleans, Louisiana, lie approximately on the same meridian. Memphis has latitude 35°N and New Orleans has latitude 30°N. Find the distance between these

Geometric applications to the cross product, Geometric Applications to the ...

Geometric Applications to the Cross Product There are a so many geometric applications to the cross product also.  Assume we have three vectors a → , b → and c → and we make

Determine the value of the unknown side of a right triangle, Determine the ...

Determine the value of the unknown side of a right triangle: The two legs of a right triangle are 5 ft and 12 ft.  How long is the hypotenuse? Now Let the hypotenuse be c ft.

International marketing, what are challenges and solution of international ...

what are challenges and solution of international marketing

What is the value of m+n, Every point (x,y) on the curve y=log2 3x is trans...

Every point (x,y) on the curve y=log2 3x is transferred to a new point by the following translation (x',y')=(x+m,y+n), where m and n are integers. The set of (x',y') form the curve

Statistical estimation, Statistical estimation This is the procedure of...

Statistical estimation This is the procedure of using statistic to estimate a population parameter This is divided into point estimation whereas an estimate of a population

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