Given,

• Direction Ratios of Line1 are proportional to (1,-2,1)

• Direction Ratios of Line2 are proportional to (4,3,2)

So we can say that,

Direction ratios of line1

a₁ = 1 × k , b₁ = (-2) × k and c₁ = 1 × k

a₁ = k , b₁ = -2k and c₁ = k

Direction ratios of line2

a₂ = 4 × p , b₂ = 3 × p and c₂ = 2 × p

a₂ = 4p , b₂ = 3p and c₂ = 2p

Now, the angle between the lines with direction ratios a₁, b₁, c₁ and a₂, b₂, c₂ is given by

By using this formula,

cos θ = 0

θ = 90°

The angle between the lines is 90°.