The direction cosines x,y,z of a line are connected by a relation (x+y)2−a2=2xy−z2 Thena2+5a+2019=

If x,y,zare direction cosines of a line then x2+y2+z2=1Consider the equation (x+y)2−a2=2xy−z2Expand and then simplify x2+y2+2xy−a2=2xy−z2⇒x2+y2+z2=a2⇒a2=1It implies that a=1Hence the value of a2+5a+2019 is 1+5+2019=2025=45