Question

Find the position vector of a point T which divides the line joining two points A and B whose position vectors are i j k ˆ 2ˆ − ˆ − 3 and i j k ˆ − 5ˆ + 2 ˆ − 5 in the ratio 3:2 (i) internally (ii) externally
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Answer 1

Answer:

hlo mate here's your answer

Step-by-step explanation:

The position vector of pointR

dividing the line segment joining two points

P

andQin the ratio

m:

n

is given by:

i. Internally:

m+n

m Q +n P

ii. Externally:

m−n

m Q −n P

Position vectors of

P

and

Q

are given as:

OP =

i

^+

2j

^−

k

^

and OQ=

− i

^ +

j

^ +

k

^

(i) The position vector of point

Rwhich divides the line joining two points PandQinternally in the ratio

2:

1

is given by,

OR=

2+1

2(− i

^ + j

^ + k

^ )+1( i

^ +2 j

^ − k

^ )

=

3

−2 i

^ +2 j

^ + k

^ +( i

^ +2 j

^ − k

^ )

=

3

− i

^ +4 j

^ + k

^

=

−

3

1

i

^+

3

4

j

^+

3

1

k

^

(ii) The position vector of point

Rwhich divides the line joining two points PandQexternally in the ratio

2:

1

is given by,

OR=

2−1

2(− i

^ + j

^ + k

^ )−1( i

^ +2 j

^ − k

^ )

=

(−2 i

^ +

2j

^+

2k

^)−

( i

^ +

2j

^−

k

^ )

=

−3 i

^ +

3 k

^

Answer verified by Toppr

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