Question

If three points with position vectors as $(1,a,b)$; $(a,2,b)$ and $(a,b,3)$ are collinear in space, then the value of $a+b$ is

• A. 3
• B. 4
• C. 5
• D. none

Answer 1

The correct option is B 4

$A(1,a,b);B(a,2,b);C(a,b,3)AB:BC=\lambda :1\Rightarrow \frac{\lambda C_{x,y,z}+A_{x,y,z}}{\lambda +1}=B_{x,y,z}\frac{\lambda a+1}{\lambda +1}=a\left(1\right)\frac{\lambda b+a}{\lambda +1}=2\left(2\right)\frac{3\lambda +b}{\lambda +1}=b\left(3\right)\Rightarrow a=1andb=3\left(from1and3\right)\Rightarrow a+b=4$