Let c be a vector perpendicular to the vectors a=i+j-k and b=i+2j+k. If c. (i + j + 3k) = 8 then the value of c. (a x b) is equal to......... c. (a x b) is equal to.........

If a = αi + βj + 3k, b = -βi - αj - k and c = i - 2j - k such that a ⋅ b = 1 and b ⋅ c = -3, then (1/3)((a × b) ⋅ c) is equal to.....

Let x₀ be the point of local maxima of f(x) = a · (b × c) where a = xî − 2ĵ + 3k, b = −2î + xĵ − k and c = 7î – 2ĵ + xk. Then the value of a · b + b · c + c · a at x = x₀ is