Let x R and ₂ x>0 . Then, the vectors A = (2, ₂ x, s ) and B = ( ₂ x, s, ₂ x ) include an acute angle if

Step-by-step solution

aligned & (b) Given, A=2 i + ₂ x j +s k & B = ₂ x i +s j + ₂ x k aligned Let the angle between A and B be , then = A B | A || B | = 2 ₂ x+s ₂ x+s ₂ x |A||B| ' ' will be acute angle if >0 , array lc i.e. & 2 ₂ x+2 s ₂ x |A||B| >0 & 2 ₂ x+2 s ₂ x>0 2 ₂ x^ s+1 >0 & x^ s+1 >2^ & x^ s+1 >1 array array ll & x^ s+1 >x^ & 1+s>0 [ 2 ₂ x>0 . always ] & 2 c s>-1 array