Find the position vector of a point R which divides the line joining the points Pi-2j-k and Q-i-j-k in the ratio 2-1 internally-

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Standard XII

Mathematics

Direction Cosines

Find the posi...

Question

Find the position vector of a point R which divides the line joining the points $P (ˆ i + 2 ˆ j - ˆ k)$ and $Q (- ˆ i + ˆ j + ˆ k)$ in the ratio 2:1 internally.

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Solution

Given,
$- - \to O P = ˆ i + 2 ˆ j - ˆ k$ and $- - \to O Q = - ˆ i + ˆ j + ˆ k$
Let R divides PQ internally in the ratio 2:1. Then, position vector of R
$= \frac{2 (- ˆ i + ˆ j + ˆ k) + 1 (ˆ i + 2 ˆ j - ˆ k)}{2 + 1}$

$= \frac{- ˆ i + 4 ˆ j + ˆ k}{3}$

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Similar questions

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

Q. Assertion :Position vector of a point R, which divides the line joining the points

P (ˆ i + 2 ˆ j - ˆ k)

and

Q (- ˆ i + ˆ j + ˆ k)

in the ratio 2 : 1 internally is

\frac{- 1}{3} ˆ i + \frac{4}{3} ˆ j + \frac{1}{3} ˆ k

Reason:

\to r = \frac{m \to b - n \to a}{m - n}

Q. Find the position vector of a point R which divides the line segment joining points

P (\hat{i} + 2 \hat{j} + \hat{k}) and Q (- \hat{i} + \hat{j} + \hat{k})

in the ratio 2:1.
(i) internally
(ii) externally

Q. 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 (ii) externally

Q. 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
(ii) externally

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Find the position vector of a point R which divides the line joining the points P(ˆi+2ˆj−ˆk) and Q(−ˆi+ˆj+ˆk) in the ratio 2:1 internally.

Given,−−→OP=ˆi+2ˆj−ˆk and −−→OQ=−ˆi+ˆj+ˆkLet R divides PQ internally in the ratio 2:1. Then, position vector of R=2(−ˆi+ˆj+ˆk)+1(ˆi+2ˆj−ˆk)2+1=−ˆi+4ˆj+ˆk3

Find the position vector of a point R which divides the line joining the points $P (ˆ i + 2 ˆ j - ˆ k)$ and $Q (- ˆ i + ˆ j + ˆ k)$ in the ratio 2:1 internally.

Given,
$- - \to O P = ˆ i + 2 ˆ j - ˆ k$ and $- - \to O Q = - ˆ i + ˆ j + ˆ k$
Let R divides PQ internally in the ratio 2:1. Then, position vector of R
$= \frac{2 (- ˆ i + ˆ j + ˆ k) + 1 (ˆ i + 2 ˆ j - ˆ k)}{2 + 1}$

$= \frac{- ˆ i + 4 ˆ j + ˆ k}{3}$