Why Does the Projection of Vector A on B Not Equal Zero?

AI Thread Summary
The projection of vector A(1,0) on vector B(-1,0) is not zero because the vectors are opposite, not perpendicular. A projection results in a negative value when the vectors point in opposite directions, as seen in this case where the projection equals -1. The dot product is zero only when vectors are perpendicular, which is not applicable here. Understanding projections involves determining the magnitude of one vector in the direction of another, but the application must consider their directional relationship. Thus, the confusion arises from misinterpreting the conditions for zero projection and dot product.
amaresh92
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greetings,
consider two vector as it is A(1,0) and B(-1,0). now if we find the projection of A on B we should get zero but its coming -1.where i am going wrong?
advanced thanks.
 
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What's the condition for dot products to be zero?
 
Hi amaresh92! :smile:

You're not going wrong.
The projection is not supposed to come out as zero, since the vectors are opposite.

Repeating Ibix, do you know what it means if the projection is zero?
 
I like Serena said:
Hi amaresh92! :smile:
Repeating Ibix, do you know what it means if the projection is zero?

what i have understood is we find projection of one vector to another when we need to find the magnitude of one vector in the direction given by another vector.

if its wrong then what is dot product and projections are ?

any help will be appreciated
thanks
 
Your understanding appears to be correct. Your application to this particular problem is wrong.

Your vector A points due East. Which way is B pointing? How far in an easterly direction is that, ignoring any northerly or southerly motion?
 
The dot product and projection are zero if and only if the vectors are perpendicular.

Opposite vectors are not perpendicular - they are in the same (but opposite) direction.
 

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