Question

If the distance between the points $(7,1,-3)$ and $(4,5,\lambda )$ is $13$ units, then what is one of the values of $\lambda$?

• A. $20$
• B. $10$
• C. $9$
• D. $8$

Answer 1

Answer: (C)

$9$

Given two points A(7,1,-3) and B(4,5,$\lambda$)

total distance=13units ,$\lambda$ =?

distance of AB $=\sqrt{(x_2-x_1{)}^2+(y_2-y_1{)}^2+(z_2-z_1{)}^2}13=\sqrt{(4-7{)}^2+(5-1{)}^2+(\lambda +3{)}^2}169=9+16+[{\lambda }^2+6\lambda +9]{\lambda }^2+6\lambda +9=144\Rightarrow {\lambda }^2+6\lambda -135=0\therefore \lambda =9,-15\therefore \lambda =9$