HSC Science (Computer Science) 12th Board ExamMaharashtra State Board
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# Solution for If point C (c)( divides the segment joining the points A(a) and B(b) internally in the ratio m : n, then prove that c=(mb+na)/(m+n) - HSC Science (Computer Science) 12th Board Exam - Mathematics and Statistics

#### Question

If point C (barc) divides the segment joining the points A(bara) and  B(barb) internally in the ratio m : n, then prove that barc=(mbarb+nbara)/(m+n)

#### Solution

Given that C(vecc) divides the segment joining the points A (veca) and B (vecb)

internally in the ratio m : n

We need to prove that vecc=(mvecb+nveca)/(m+n)

Consider the following figure

since (

n x length (AC)=m X length (BC)

nvec(AC)=mvec(CB)

n(vec(OC)-vec(OA))=m(vec(OB)-vec(OC))

n(vecc-veca)=m(vecb-vecc)

nvecc-nveca=mvecb-mvecc

(n+m)vecc=mvecb+nveca

vecc=(mvecb+nveca)/(m+n)

Hence proved.

Is there an error in this question or solution?

#### APPEARS IN

2014-2015 (March) (with solutions)
Question 2.1.3 | 3 marks

#### Video TutorialsVIEW ALL [2]

Solution for question: If point C (c)( divides the segment joining the points A(a) and B(b) internally in the ratio m : n, then prove that c=(mb+na)/(m+n) concept: Section formula. For the courses HSC Science (Computer Science), HSC Science (General) , HSC Arts, HSC Science (Electronics)
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