Question

If (a, a + b, a + b + c) is one set of direction ratios of the line joining (1, 0, 0) and (0, 1, 0), then find a set of values of a, b, c.

Answer 1

Let A be the point (1, 0, 0) and B be the point (0, 1, 0) (i.e.,) vector OA = i and vector OB = j 

Then vector AB = vector (OB - OA) = j - i = - i + j 

= (-1, 1, 0) 

= (a, a + b, a + b + c) 

⇒ a = -1, a + b = 1 and a + b + c = 0 

Now a = -1 ⇒ -1 + b = 1 ;a + b + c = 0

⇒ b = 2; -1 + 2 + c = 0 ⇒ c + 1 = 0 

⇒ c = -1 

∴ a = -1; b = 2; c = -1. 

Note: If we taken vector BA then we get a = 1, b = -2 and c = 1.