A) \[3:10\]
B) \[10:3\]
C) \[2:3\]
D) \[3:2\]
Correct Answer: A
Solution :
[a] The plane \[x-2y+3z=17\]divides the line joining the points \[\left( 2,-4,-7 \right)\] and \[\left( 3,-5,8 \right)\] in the ratio \[\lambda :1.\] Let P be the dividing point \[\therefore P\equiv \left( \frac{3\lambda -2}{\lambda +1},\frac{-5\lambda +4}{\lambda +1},\frac{8\lambda +7}{\lambda +1} \right)\] Since point P lies on the given plane \[x-2y+3z=17.\] \[\Rightarrow \frac{3\lambda -2}{\lambda +1}-2.\frac{(-5\lambda +4)}{\lambda +1}+3.\left( \frac{8\lambda +7}{\lambda +1} \right)=17\] \[\Rightarrow 3\lambda -2+2(5\lambda ,-4)+3(8\lambda +7)=17(\lambda +1)\] \[\Rightarrow 3\lambda -2+10\lambda -8+24\lambda +21=17\lambda +17\] \[\Rightarrow 37\lambda -17\lambda =17-11\] \[\Rightarrow 20\lambda =6\] \[\Rightarrow \lambda =\frac{6}{20}=\frac{3}{10}\] Hence, option [a] is correct.
You need to login to perform this action.
You will be redirected in
3 sec
