Question

If $A(2,1,9),B(-4,1,-3),C(0,7,6)$ are the vertices of $△ABC$ and the equation of the median through $C$ is $\frac{x}{a}=\frac{y-7}{b}=\frac{z-6}{-3},$ then $|a+b|$ is equal to

• A. $9$
• B. $7$
• C. $10$
• D. $4$

Answer 1

The correct option is B $7$

Let $F$ be the mid point of side $AB,$ then D.R's of $CF$ and the D.R's of the line $\frac{x}{a}=\frac{y-7}{b}=\frac{z-6}{-3}$ will be same.
Now $F=$ mid point of $AB=(-1,1,3)$,
Now,D.R'S of $CF=(-1,-6,-3)$
Hence, $(a,b,-3)=(-1,-6,-3)$
So, $|a+b|=7$