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The dot product

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

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• Could you also think of the projection of vector A as a component of A?
• If you think of B vector as an axis (either x-axis or y-axis), yes you could think of the projection as a component of A (either Ax or Ay)
• 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. :)
• 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
• 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.
• I could'nt understand why we should take component of A along B.
• 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.
• How do you find U if you're given V and the dot product?

ie: v=(4,6), u*v=38, find u