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### Course: Class 11 Physics (India)>Unit 10

Lesson 1: Introduction to work

# The dot product

Introduction to the vector dot product. Created by Sal Khan.

## Want to join the conversation?

• so the dot product of two vectors does not have a direction?
• Yes, the dot product of two vectors is a scalar.
• At
DOT PRODUCT ends up in a SCALER QUANTITY
WHY ?
• This is a great question! The dot product has a magnitude but no direction. If it were to have a direction, what would be the most sensical direction to assign to it? The dot product measures how much the two vectors share with each other. How about the direction of vector a? But we could just as easily choose the direction of vector b. How about the weighted average of vector a and b? This makes sense, and will still be perpendicular to the cross product vector, just like how sine and cosine are perpendicular. Perhaps this definition is how it SHOULD be. :)
• I could'nt understand why we should take component of A along B.
• why we dont use sin instead of cos
• sin and cos represent two different angles.
sin means opposite over hypotenous while cos means adjacent over hypoteneous
• Why is this different than the usual dot product in linear algebra? I did not see cos mentioned when I learned about dot product in linear algebra.
(1 vote)
• I bet you did. It's the same dot product.
• I don't understand what the number you get at the end of calculating the dot product represents? Also, if I flip the terms around, do I get a different answer? is a dot b the same as b dot a?
(1 vote)
• order does not matter with the dot product. It does matter with the cross product.

The number you are getting is a quantity that represents the multiplication of amount of vector a that is in the same direction as vector b, times vector b. It's sort of the extent to which the two vectors are working together in the same direction.
• How does W as a dot product translate back to Work = Force * Distance?
• How do you find U if you're given V and the dot product?

ie: v=(4,6), u*v=38, find u
• You can't. At least not with only that information. However you can find a relationship between the x and y in u = (x,y)... i.e. you can say that 4x+6y=38.
• What's the benefit of using dot product instead of just sticking with the old definition of using the components using trigonometry along the direction we need? In the electromagnetic theory lesson, we are revisiting these vector concepts but I realise in the past physics lessons I've never questioned this because I've never needed to use dot product definition rather than questions specifically asking for it, because I could do the same thing with trigonometry. This is not same for cross-product however, it is a totally new concept specific for vectors only and I used it frequently because there are no alternatives.
My exact question is why we need a new definition for something we know already or is it something going to make future more complex calculations easier which I don't have much idea yet.