Vector Algebra Question 100
Question: If the middle points of sides BC, CA & AB of triangle ABC are respectively D, E, F then position vector of centre of triangle DEF, when position vector of A, B, C are respectively $ \hat{i}+\hat{j},\hat{j}+\hat{k},\hat{k}+\hat{i} $ is
Options:
A) $ \frac{1}{3}(\hat{i}+\hat{j}+\hat{k}) $
B) $ (\hat{i}+\hat{j}+\hat{k}) $
C) $ 2(\hat{i}+\hat{j}+\hat{k}) $
D) $ \frac{2}{3}(\hat{i}+\hat{j}+\hat{k}) $
Show Answer
Answer:
Correct Answer: D
Solution:
- [d] The position vector of points D, E, F are respectively $ \frac{\hat{i}+\hat{j}}{2}+\hat{k},\hat{i}+\frac{\hat{k}+\hat{j}}{2} $ and $ \frac{\hat{i}+\hat{k}}{2}+\hat{j} $ So, position vector of centre of $ \Delta DEF $ $ =\frac{1}{3}[ \frac{\hat{i}+\hat{j}}{2}+\hat{k}+\hat{i}\frac{\hat{k}+\hat{j}}{2}+\frac{\hat{i}+\hat{k}}{2}+\hat{j} ] $ $ =\frac{2}{3}[ \hat{i}+\hat{j}+\hat{k} ] $
BETA
