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

Mutually exclusive events, Mutually Exclusive Events A set of events i...

Mutually Exclusive Events A set of events is said to be mutually exclusive if the occurrence of any one of the events precludes the occurrence of any of the other events for i

Repetition need not be boring-ways to aid learning maths, Repetition Need N...

Repetition Need Not Be Boring :  From an early age on, children engage in and learn from repetitive behaviour, such as dropping and picking up things, opening and closing boxes an

Numerical analysis and computer techniques, write a fortan programme to gen...

write a fortan programme to generate prime number between 1 to 100

Help, I really need help with 30 60 90 right triangles and my last tutor di...

I really need help with 30 60 90 right triangles and my last tutor did not make sense to me so can you please help

first and third quartiles, From the data given below calculate the value o...

From the data given below calculate the value of first and third quartiles, second and ninth deciles and forty-fifth and fifty-seventh percentiles.

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