If the vectors , ,  are collinear if λ equals

Concept:

Conditions of collinear vector:

• Three points with position vectors  are collinear if and only if the vectors  and  are parallel. ⇔ 
• If the points (x1, y1, z1), (x2, y2, z2) and (x3, y3, z3) be collinear then 

Solution:

We know that, If the points (x1, y1, z1), (x2, y2, z2), and (x3, y3, z3) be collinear then 

Given  , ,  are collinear

∴ 

⇒ 1 (-20 + 14) – (2) (-5λ + 21) + 3 (-2λ + 12) = 0

⇒ -6 + 10λ – 42 - 6λ + 36  = 0

⇒ 4λ = 12

∴ λ = 3