The cartesian equation of the line through the points (4,3,5) and which is parallel to the vector 2 ̂i + 5 ̂j + 2 ̂k is-
Answer & explanation
Correct answer: option 4
We have vector a = 4 ̂i + 3 ̂j + 5 ̂k
and vector b = 2 ̂i + 5 ̂j + 2 ̂k
Therefore vector equation of the line is given by-
vector r = a+λb
⇒ r = (4 ̂i + 3 ̂j + 5 ̂k)+λ (2 ̂i + 5 ̂j + 2 ̂k)
⇒ r = (4+ 2λ) ̂i + (3+5λ) ̂j + (5+ 2λ) ̂k
⇒ x ̂i + y ̂j +z ̂k = (4+ 2λ) ̂i + (3+5λ) ̂j + (5+ 2λ) ̂k
Eliminating λ, we get
(x-4)/2 = (y-3)/5 = (z-5)/2