Find a vector c c1c2c3 which is orthogonal to both a 1058

Find a vector c = (c1,c2,c3) which is orthogonal to both a = (-10,-5,8) and b = (-5,-3,-4) and such that c1 = -1

for orthogonal vectors, their dot product must be equal to zero c.a = (-1,c2,c3).(-10,-5,8) = 10 - 5c2 + 8c3 = 0 5c2 - 8c3 = 10...........(1) c.b = (-1,c2,c3).(-5,-3,-4) = 5 - 3c2 - 4c3 = 0 3c2 + 4c3 = 5...........(2) solving (1) & (2) 11c2 = 20 c2 = 20/11 c3 = -5/44 hence vector c is (-1, 20/11, -5/44)