A unit vector perpendicular to both i + j + k and 2 i + j +3 k is

Step-by-step solution

Given vectors b = i + j + k , c =2 i + j +3 k Let the unit vector a= a |a| a b =0 (a₁ i +a₂ j +a₃ k ) | a | ( i + j + k )=0 array lc & a₁+a₂+a₃=0 and & a c =0 & (a₁ i +a₂ j +a₃ k ) | a | (2 i + j +3 k )=0 array 2 a₁+a₂+3 a₃=0 (iii) On solving Eqs. (ii) and (iii) by cross multiplication method aligned a₁ 3-1 &= a₂ 2-3 = a₃ 1-2 a₁ 2 &= a₂ -1 = a₃ -1 aligned From Eq. (i), we get a= 2 i-j-k 4+1+1 = (2 i-j-k) 6