How do i calculate this dot product

AI Thread Summary
To calculate the dot product of the vectors i and 1/√2(i + j), one must apply the formula for the dot product, which involves multiplying corresponding components and summing the results. The vectors can be represented as (1, 0) and (1/√2, 1/√2). Using the distributive property, the calculation yields i·i = 1 and i·j = 0, leading to a final result of 1/√2. Understanding that perpendicular vectors yield a dot product of zero and parallel vectors yield one is crucial for this calculation. The discussion emphasizes the importance of correctly identifying vector components in the dot product process.
vande060
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Homework Statement



i dot 1/√2( i + j)


Homework Equations





The Attempt at a Solution



I think that perpendicular vectors are zero are dotted together, and parallel vectors dotted are 1. I am tempted do do the distributive property where i dot i is 1 and i dot j is zero, but I have a feeling this is not right
 
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i.i = 1

So you are essentially correct.
 
The dot product of two vectors with components (a,b,c) and (d,e,f) is simply the sum of the products of the corresponding components. In this case, a*d + b*e + c*f.

These vectors written in the form using unit vectors to represent the component directions are: ai + bj + ck, and di + ej + fk, where i,j,k are the unit vectors. The components are still (a,b,c) and (d,e,f).

It looks like your vectors are 2D vectors, (1,0) and (1/√2, 1/√2).
 
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