A) 0
B) 1
C) -1
D) 2
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, \[\frac{\overrightarrow{m{{r}_{1}}}+\overrightarrow{n{{r}_{2}}}}{m+n}=m{{r}_{1}}+n{{r}_{2}}\] \[\Rightarrow m+n=1\]
You need to login to perform this action.
You will be redirected in
3 sec
