Final answer:
In vector algebra, multiplying a vector à by a scalar does not yield an equation like 7 = 7, but instead scales the vector's magnitude by the scalar while its direction remains constant.
Step-by-step explanation:
The question pertains to whether the vector equation ã = à x 7 implies that the scalar multiplication always results in the identity 7 = 7. In vector algebra, when you multiply a vector by a scalar, you're simply scaling the vector by that factor. The vector's direction remains unchanged, and its magnitude is multiplied by the scalar. This is consistent with the rule (xa)b = xa.b, which states that a vector x multiplied by a scalar a and then by scalar b is equivalent to multiplying the vector by the product of the two scalars (in this case ab).
In the given equation, if à is a vector and 7 is a scalar, the multiplication à x 7 would result in a new vector seven times as long as à but pointing in the same or the opposite direction (depending on whether the scalar is positive or negative). It does not imply that 7 = 7, which is a scalar equation, and is true independently of any vector operations.