Solve the Problem $a , b$ And $c$ That Make Gradient Field

Short Answer

Solve the problem.
-Find the values of $a , b$ and $c$ that make $F = - 9 y ^ { 4 } z ^ { 10 } \left( a x ^ { 7 } + b x ^ { 8 } \right) i - 36 y ^ { 3 } z ^ { 10 } \left( 7 x ^ { 8 } - 7 x ^ { 9 } \right) j + c y ^ { 4 } z ^ { 9 } \left( 7 x ^ { 8 } - 7 x ^ { 9 } \right) \mathbf { k } a$ gradient field.