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QUESTION: i have an expression which has a scalar quantity in left hand side is equal to dot product of two vectors whole square[ex. g=constant*(a.b)^2], where a and b are vectors and g is a scalar. How to remove the square of the dot product?
ANSWER: Since the square looks like it is outside the dot product,
it can be said if your equation is g = k(a∙b)²,
then what can be said it that √(g/k) = a∙b.
---------- FOLLOW-UP ----------
QUESTION: thank you sir for your suggestion. now the next question that follow up the previous one is how to convert the same equation as a sum of two vectors?
example: sqrt(g/k)= a+b, where a and b are vectors.
The dot product of two vectors is an integer.
However, the sum of two vectors is still a vector.
It makes no sense to say that a numer is a vector.
If you squared both sides, you would have g/k = (a+b)²,
but since a and b are vectors, (a+b)² is a matrix.
You could then say that g = k(a+b)²,
but that is a single value is equal to a matrix.
Maybe g is the |k(a+b)²|.
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