If a =x^2 i +x j +3 k and b =x i -4 j +2 k and a b >6 then

Step-by-step solution

Given, aligned & a =x^2 i +x j +3 k & b =x i -4 j +2 k aligned aligned & a b >6 & (x^2 i +x j +3 k )(x i -4 j +2 k )>6 & x^2 x+(x)(-4)+3(2)>6 aligned [ a b = a ₁ a ₂+ b ₁ b ₂+ c ₁ c ₂ . , where . a =a₁ i +b₁ j +c₁ k and b =a₂ i +b₂ j +c₂ k ] array rrr & x^3-4 x+6>6 & x^3-4 x+6-6>0 & x^3-4 x>0 & x (x^2-4 )>0 & x(x-2)(x+2)>0 array Using wavy curve method critical points are x=0,2,-2 Solution is x (-2,0) (2, ) .