If 2x−3y+4z=0,5x−2y−z=0,21x−8y+az=0has infinitely many solutions, then a=

The condition for a homogeneous system to have infinitely many solutions is Δ=0⇒2-345-2-121-8a=0⇒2-2a-8+35a+21+4-40+42=0⇒-4a-16+15a+63+8=0⇒11a+55=0⇒11a=-55⇒a=-5