Thursday, 18 June 2015

VECTORS: Significance &Application of Cross product and Dot product.

DOT PRODUCT.

|||| A.B = |A||B|Cos(angle).

EXAMPLE

Haven't you wondered why cos?

|||| Like I said in my post on TRIGONOMETRY, Cos comes into equations when two forces work hand in hand-in-hand with each other to produce the net resultant.

|||| Dot product is also similar. It is used when Two forces A and B produce maximum effect or impact when work together 'in a line'.

|||| A.B = |A||B| Cos(angle) means that the resulting force  is due to

1] Force of A

2] Force of B

3] Angle in which A and B are colliding into each other.

|||| Cos in the equation is like telling that, "if you want maximum impact, place A are B as parallel to each other as possible".

|||| For example, if you are rowing a river, row as parallel as possible to the flow of the river to get maximum results.

|||| Multiplication again means combination. Thus A and B and the angle of  A and B working together as if are combining to form the net result.

CROSS PRODUCT
|||| Cross-product is a measure of how much perpendicular two objects work in relation to each other.

|||| Cross product comes into picture whenever two objects work against each other, completely out of line and produce maximum impact when perpendicular.

|||| Now imagine the same boat and the same river, but this time instead of measuring the velocity of the river, you want to measure the friction between the boat and the river .

|||| In other words, instead of trying to measure maximum velocity, you want to produce maximum friction between your boat and the river.

|||| Now this will happen when your boat is at 90 degrees to the flow of the river.

|||| Thus maximum friction is when your boat is at cross with the river.

|||| Thus A X B = |A||B| Sin (angle).

|||| Sin as I said comes into those equations where max impact is at perpedicular angles or when two things work against each other or out of alignment.

|||| Thus we can say that Cross-product comes when we have to measure those forces like friction which happen when two objects work against each other and Dot-product comes when we have to measure those forces like total additive velocity which happen when two forces work hand-in-hand with each other.

Hope this helps

BINNOY
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THE ABOVE IS A EXCERPT FROM A BOOK AVAILABLE FOR PURCHASE (5\$) AT THE FOLLOWING LINK
VISUALIZING MATHS.PDF

AVAILABLE FOR PURCHASE FOR 5\$ (INR 300) HERE (PDF)

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I hardly understood Math in school. In fact was on the verge of dropping the subject I loved the most because as much as I loved the theory of it, I could not understand the math involved in it. However I loved the subject too much to be able to live without. Hopelessly, I was continuing my love-affair with it.

Then one day....a miracle happened,....while applying a certain formula again and again.....I came to know its significance. Slowly and steadily....other equations also started clicking. I got to see a strong relationship between Maths and the Physics it was pointing towards. They both were the same. Maths was just an easy language to express a physical phenomenon. And a bit more to that in the sense that it could even predict the behaviour of a certain physical phenomenon. Equations now as if came to life.

Every equation now had as if something to say. A burning urge to share these things with the world aflamed within me. So that no one has to give up the subject that he or she loves the most.
The book on visualizing maths thus got written as a sprout of inspiration. The blog followed. Both these are dedicated to you and all such similar minds searching for answers.

Visualizing Math & Physics is a blog dedicated to you and all such similar minds searching for answers.

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CONTACT
binnoypanicker@gmail.com

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A GOOD EXAMPLE OF DOT PRODUCT
ANOTHER EXPLANATION OF DOT PRODUCT

DOT-PRODUCT AND CROSS-PRODUCT LINK FROM PHYSICS CLASSROOMS.COM

DOT PRODUCT EXAMPLE IS GOOD