JEE Main & Advanced
Mathematics
Vector Algebra
Question Bank
Critical Thinking
question_answer
The points D, E, F divide BC, CA and AB of the triangle ABC in the ratio 1 : 4, 3 : 2 and 3 : 7 respectively and the point K divides AB in the ratio \[1:3\], then \[(\overrightarrow{AD}+\overrightarrow{BE}+\overrightarrow{CF})\,\,:\,\,\overrightarrow{CK}\] is equal to [MNR 1987]
A)1 : 1
B)2 : 5
C)5 : 2
D)None of these
Correct Answer:
B
Solution :
Let \[\overrightarrow{AB}=\mathbf{a},\] \[\overrightarrow{AC}=\mathbf{b}\]
So,\[\overrightarrow{AD}=\frac{4\mathbf{a}+\mathbf{b}}{5},\]\[\overrightarrow{AE}=\frac{2\mathbf{b}}{5},\] \[\overrightarrow{AF}=\frac{3\mathbf{a}}{10},\] and \[\overrightarrow{AK}=\frac{\mathbf{a}}{4}\]