How do i calculate this dot product

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SUMMARY

The discussion focuses on calculating the dot product of the vector expression i dot 1/√2( i + j). The correct approach involves recognizing that the dot product of two vectors is the sum of the products of their corresponding components. Specifically, for the vectors (1,0) and (1/√2, 1/√2), the calculation confirms that i dot i equals 1 and i dot j equals 0, leading to a final result of 1/√2.

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  • Understanding of vector notation and components
  • Familiarity with the concept of dot product
  • Knowledge of unit vectors i, j, and k
  • Basic algebraic manipulation skills
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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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