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Section Formula - Practice Questions & MCQ

Edited By admin | Updated on Sep 18, 2023 18:34 AM | #JEE Main

Quick Facts

  • Section Formula is considered one of the most asked concept.

  • 14 Questions around this concept.

Solve by difficulty

If C is the mid point of AB and P is any point outside AB, then

If position vector of a point A is a +2b and a divides Ab in the ratio 2:3, then the position vector of B is :

What is the position vector of a point which divides point A with position vector, OA=2i^j^+3k^ and point B with position vector OB=2i^+3j^3k^ in the ratio 2:3 ?

Concepts Covered - 1

Section Formula

Let A and B be two points represented by the position vectors OA and OB, respectively, with respect to the origin O. 

Let R be a point that divides the line segment joining the points A and B in the ratio m: n. 

Internal Division

If R divides AB internally in the ratio m: n, then the position vector of R is given by  OR=mb+nam+n

Proof : 

Let O be the origin. Then OA=a~ and OB=b~. Let r~ be the position vector of R which divides AB internally in the ratio m:n. Then
or
ARRB=mnn(AR)=m(RB)

Now from triangles ORB and OAR, we have
RB=OBOR=b~r~
and,
AR=OROA=r~a~

Therefore, we have
or
m( b~r~)=n(r~a~)r=mb+nam+n

Hence, the position vector of the point R which divides A and B internally in the ratio of m: n is given by

OR=mb+nam+n

External Division

If R divides AB externally in the ratio m: n, then the position vector of R is given by OR=mbnamn

NOTE:

If R is the midpoint of AB, then m = n. And therefore, the midpoint R of AB , will have its position vector asOR=a+b2

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Section Formula

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