If the angle between the lines whose direction ratios are (2,-1,2) and (x, 3,5) is 4 , then the smaller value of x is

Step-by-step solution

Given direction ratios are (2,-1,2) and ( x , 3,5) We know that the angle between the lines whose direction ratios are (a₁, b₁, c₁ ) and (a₂, b₂, c₂ ) is aligned & = a ₁ a ₂+ b ₁ ~b ₂+ c ₁ c ₂ a ₁^2+ b ₁^2+ c ₁^2 a ₂^2+ b ₂^2+ c ₂^2 & 4 = 2 x -3+10 4+1+4 x ^2+9+25 = 2 x +7 9 x ^2+34 aligned 1 2 = 2 x+7 3 x^2+34 2 x+7=3 x^2+34 2 4 x ^2+49+28 x = 9 ( x ^2+34 ) 2 (Squaring on both sides) aligned & 2 (4 x^2+49+28 x )=9 x^2+306 & 8 x^2+98+56 x=9 x^2+306 & x^2-56 x+208=0 aligned aligned & x = 56 3136-812 2 = 56 48 2 =28