You can accomplish that without requiring a special-purpose function.

In E3, try this (and copy it to the rest of your rows):

=sum(arrayformula(B3:D3*B$2:D$2))

You can read about arrayformula here.

As long as you introduce new columns between B and D, this formula will automatically adjust. If you add new columns outside of that range, you'll need to edit (and cut & paste).

On it's own, arrayformula(B3:D3*B$2:D$2) operates over each value in B3:D3 in turn, multiplying it by the corresponding value in B$2:D$2. (Note the use of absolute references to 'lock down' to row 2.) The result in this case is three values, [10,3,0], arranged horizontally in three rows because that matches the dimensions of the ranges.

The enveloping sum() function adds up the values of the array produced by arrayformula, which is 13 in this case.

As you copy that formula to other rows, the relative range references get updated for the new row.