Vector Algebra Question 126
Question: If $ \overset{\to }{\mathop{r_1}},,\overset{\to }{\mathop{r_2}},,\overset{\to }{\mathop{r_3}}, $ are the position vectors of three collinear points and scalars m and n exist such that $ \overset{\to }{\mathop{r_3}},=m\overset{\to }{\mathop{r_1}},+n\overset{\to }{\mathop{r_2}}, $ , then what is the value of (m+n)?
Options:
A) 0
B) 1
C) -1
D) 2
Show Answer
Answer:
Correct Answer: B
Solution:
- [b] Since $ \overset{\to }{\mathop{r_1}},,\overset{\to }{\mathop{r_2}}, $ and $ \overset{\to }{\mathop{r_3}}, $ are the position vector of three collinear points. Thus $ \overset{\to }{\mathop{r_3}}, $ is the position vector of the point which divides the joining of points whose position vectors are $ \overset{\to }{\mathop{r_1}}, $ and $ \overset{\to }{\mathop{r_2}}, $ in the ratio m:n. So, $ \overset{\to }{\mathop{r_3}},=\frac{m\overset{\to }{\mathop{r_1}},+n\overset{\to }{\mathop{r_2}},}{m+n} $ But as given, $ \overset{\to }{\mathop{r_3}},=m\overset{\to }{\mathop{r_1}},+n\overset{\to }{\mathop{r_2}}, $ So, $ \frac{\overrightarrow{mr_1}+\overrightarrow{nr_2}}{m+n}=mr_1+nr_2 $
$ \Rightarrow m+n=1 $
BETA
