Question

(i) Find the angle between the lines having direction ratios 1, 1, 2 and √3 − 1, −√3 −1, 4

(ii) If the lines and  \(\frac{x-1}{3}=\frac{y-1}{2λ}=\frac{z-3}{2}\) and \(\frac{x-1}{3λ}=\frac{y-1}{1}=\frac{z-6}{-5}\) are perpendicular, find the value of λ

Answer 1

(i)

 

(ii) Since they are perpendicular 

a₁a₂+ b₁b₂+ c₁c₂ = 0 

⇒ 3 x 3λ + 2λ x 1 + 2x – 5 = 0 

⇒ 9λ + 2λ – 10 = 0

 ⇒ 11λ + 10 

⇒ 2 = \(\frac{-10}{11}\)