function calculate(){
	var a1 = document.getElementById("a<sub>1</sub>").value;
    var a2 = document.getElementById("a<sub>2</sub>").value;
    var a3 = document.getElementById("a<sub>3</sub>").value;
    var b1 = document.getElementById("b<sub>1</sub>").value;
    var b2 = document.getElementById("b<sub>2</sub>").value;
    var b3 = document.getElementById("b<sub>3</sub>").value;
    var i, j, k;
	if (a1 != ""  && a2 != ""  && a3 != ""  && b1 != ""  && b2 != ""  && b3 != "") {
        a1 = parseFloat(a1);
        a2 = parseFloat(a2);
        a3 = parseFloat(a3);
        b1 = parseFloat(b1);
        b2 = parseFloat(b2);
        b3 = parseFloat(b3);
        i = (a1*b1);
        j = (a2*b2);
        k = (a3*b3);
		document.getElementById("dot product").innerHTML = "dot product: " + (i+j+k);
	}
}