The angle between the lines L₁: x-5 = y+2 -5 = 5 z+24 5 and L₂: x=z, y=0 is 4 , then the value of (4 ) is

Step-by-step solution

The line L₁ is given by x-5 = y+2 -5 = z + 24/5 . The direction vector of L₁ is v₁ = i - 5 j + k . The line L₂ is given by x=z and y=0 . This can be written as x 1 = z 1 with y=0 . The direction vector of L₂ is v₂ = 1 i + 0 j + 1 k . The angle between the lines is 4 . The cosine of the angle is given by = | v₁ v₂ | | v₁ | | v₂ | . Substituting the values, ( /4) = | (1) - 5(0) + (1)| ^2 + (-5)^2 + ^2 1^2 + 0^2 + 1^2 = 1 2 . This simplifies to | + | ^2 + 25 + ^2 2 = 1 2 , which implies | + | = ^2 + 25 + ^2 . Squaring