Law of cosines - vector, Mathematics


a • b = ||a|| ||b|| cos•


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

Posted Date: 4/13/2013 2:28:29 AM | Location : United States

Related Discussions:- Law of cosines - vector, Assignment Help, Ask Question on Law of cosines - vector, Get Answer, Expert's Help, Law of cosines - vector Discussions

Write discussion on Law of cosines - vector
Your posts are moderated
Related Questions
An irrigation system uses a straight 30m sprinkler pipe which is capped at one end and arranged so that all water is released directly downwards and pivots around a central point.

suresh invested rs.1080 in shares of face value rs.50 at rs.54.After receiving dividend on them at 8% he sold them at 52.In each of the transaction he paid 2 % brokerage.Hpw much d

who created math?

( a+2b)x + (2a - b)y = 2, (a - 2b)x + (2a +b)y = 3 (Ans: 5b - 2a/10ab , a + 10b/10ab ) Ans: 2ax + 4ay = y , we get 4bx - 2by = -1 2ax+ 4ay = 5  4bx- 2by = - 1

The light on a lighthouse blinks 45 times a minute. How long will it take the light to blink 405 times? Divide 405 by 45 to get 9 minutes.

Belleville lake was originally blue because it only had 11 algae plants. then towns and farms cropped up by the lake .this cause 446 more algae plants to grow which turned the lake

If ABCD isaa square of side 6 cm find area of shaded region

1 ream uses 6% of a tree, Estimate the reams of paper used in one month in an office(may be your father, mother or neighbour), hence find the number of trees that need to be cut fo