1
Question
Find the position vector of a point R which divides the line joining two points P and Q whose position vectors are ^i+2^j−^k and −^i+^j+^k respectively, in the ratio 2:1
(i) Internally
Find the position vector of a point R which divides the line joining two points P and Q whose position vectors are ^i+2^j−^k and −^i+^j+^k respectively, in the ratio 2:1
(i) Internally
Open in App
Solution
The position vector of a point R divided the line segment joining two points P and Q in the ratio m : n is given by
Case I Internally= mb+nam+n
Case II Externally=mb−nam−n
Position vectors of P and Q are given as
OP=^i+2^j−^k and OQ=−^i+^j+^k
(i) PV of R [dividing (PQ) in the ratio m:n internally]
=m(PV of Q)+n(PV of P)m+n
Here m=2, n=1=2(PV of Q)+1[PV of P]2+1
=13[2(−^i+^j+^k)+1(^i+2^j−^k)]
=13(−^i+4^j+^k)=(−13)^i+(43)^j+(13)^k
The position vector of a point R divided the line segment joining two points P and Q in the ratio m : n is given by
Case I Internally= mb+nam+n
Case II Externally=mb−nam−n
Position vectors of P and Q are given as
OP=^i+2^j−^k and OQ=−^i+^j+^k
(i) PV of R [dividing (PQ) in the ratio m:n internally]
=m(PV of Q)+n(PV of P)m+n
Here m=2, n=1=2(PV of Q)+1[PV of P]2+1
=13[2(−^i+^j+^k)+1(^i+2^j−^k)]
=13(−^i+4^j+^k)=(−13)^i+(43)^j+(13)^k
Suggest Corrections
0
respectively, in the ration 2:1