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

find an explicit formula, (a) The generating function G(z) for a sequence ...

(a) The generating function G(z) for a sequence g n is given by G(z) = 1 - 2z/(1 + 3z)3 Give an explicit formula for g n . (b) For the sequence gn in the previous part co

Simplification, 4.4238/[1.047+{1.111*[9.261/7.777]}*1.01

4.4238/[1.047+{1.111*[9.261/7.777]}*1.01

How much more does she required to sell to meet her goal, Hanna's sales tar...

Hanna's sales target for the week is $5,000. So far she has sold $3,574.38 worth of merchandise. How much more does she required to sell to meet her goal? You must ?nd out the

Explain the algebraic expressions and equations, Explain the Algebraic Expr...

Explain the Algebraic Expressions and Equations? Writing a math problem algebraically means that you are using numbers and variables to represent relationships. "Three inche

Course work2 , (b) The arity of an operator in propositional logic is the n...

(b) The arity of an operator in propositional logic is the number of propositional variables that it acts on – for example, binary operations (e.g, AND, OR, XOR…) act on two propo

Vector function - three dimensional spaces, Vector Function The good wa...

Vector Function The good way to get an idea of what a vector function is and what its graph act like is to look at an instance.  Thus, consider the following vector function.

Simple interest, write a program C++ programming language to calculate sim...

write a program C++ programming language to calculate simple interest, with it algorithm and it flowchart

Confidence interval, Confidence Interval The interval estimate or a 'co...

Confidence Interval The interval estimate or a 'confidence interval' consists of a range as an upper confidence limit and lower confidence limit whether we are confident that a

Evaluate following unit circle, Evaluate following sin 2 ?/3   and sin (-2 ...

Evaluate following sin 2 ?/3   and sin (-2 ?/3) Solution: The first evaluation in this part uses the angle 2 ?/3.  It is not on our unit circle above, though notice that  2 ?/

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