If the direction ratios of the lines L₁ and L₂ are 2,-1,1 and 3,-3,4 respectively, then the direction cosines of a line that is perpendicular to both L₁ and L₂ are

Step-by-step solution

Let direction cosines of line that is perpendicular to both L₁ and L₂ are l, m, n , then aligned & 2 l-m+n=0 and 3 l-3 m+4 n=0 & l -4+3 = m 3-8 = n -6+3 l -1 = m -5 = n -3 & l l = m 5 = n 3 = l^2+m^2+n^2 1+25+9 & l, m, n= 1 35 , 5 35 , 3 35 . aligned