If $¯ ¯ ¯ p =^i - 2^j +^k$ and $¯ ¯ ¯ q =^i + 4^j - 2^k$ are position vectors of points $P$ and $Q$ , find the position vector of the point $R$ which divides segment $P Q$ internally in the ratio $2 : 1$

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Solution

Let $R (\to r)$ is the point which divides the line segment joining the points $P$ and $Q$ internally in the ratio $2 : 1$ .
$\to r = \frac{2 (^i + 4^j - 2^k) + 1 (^i - 2^j +^k)}{2 + 1}$
$\to r = \frac{3^i + 6^j - 3^k}{3}$
$∴ \to r =^i + 2^j -^k$
and the coordinates of the point $R$ are $(1, 2, - 1)$ .

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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
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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

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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
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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

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(i) internally
(ii) externally

Find the position vector of a point R which divides the line joining two points P and Q whose position vectors are respectively, in the ration 2:1

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(ii) externally

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If ¯¯¯p=^i−2^j+^k and ¯¯¯q=^i+4^j−2^k are position vectors of points P and Q, find the position vector of the point R which divides segment PQ internally in the ratio 2:1

Let R(→r) is the point which divides the line segment joining the points P and Q internally in the ratio 2:1.→r=2(^i+4^j−2^k)+1(^i−2^j+^k)2+1→r=3^i+6^j−3^k3∴→r=^i+2^j−^kand the coordinates of the point R are (1,2,−1).

If $¯ ¯ ¯ p =^i - 2^j +^k$ and $¯ ¯ ¯ q =^i + 4^j - 2^k$ are position vectors of points $P$ and $Q$ , find the position vector of the point $R$ which divides segment $P Q$ internally in the ratio $2 : 1$