Q. 14.2( 44 Votes )

# Find the coordinates of the point which divides the line segment joining the points (– 2, 3, 5) and (1, – 4, 6) in the ratio (i) 2 : 3 internally, (ii) 2 : 3 externally.

Answer :

Let the line segment joining the points P (-2, 3, 5) and Q (1, -4, 6) be PQ.

(i) By Section Formula,

We know that the coordinates of the point R which divides the line segment joining two points P (x_{1}, y_{1}, z_{1}) and Q (x_{2}, y_{2}, z_{2}) internally in the ratio m : n is given by:

Comparing this information with the details given in the question, we have

x_{1} = -2, y_{1} = 3, z_{1} = 5; x_{2} = 1, y_{2} = -4, z_{2} = 6 and m = 2, n = 3

So,

The coordinates of the point which divides the line segment joining the points P (– 2, 3, 5) and Q (1, – 4, 6) in the ratio 2 : 3 internally is given by:

Hence, the coordinates of the point which divides the line segment joining the points (-2, 3, 5) and (1, -4, 6) is .

(ii) By Section Formula,

We know that the coordinates of the point R which divides the line segment joining two points P (x_{1}, y_{1}, z_{1}) and Q (x_{2}, y_{2}, z_{2}) externally in the ratio m : n is given by:

Comparing this information with the details given in the question, we have

x_{1} = -2, y_{1} = 3, z_{1} = 5; x_{2} = 1, y_{2} = -4, z_{2} = 6 and m = 2, n = 3

So,

The coordinates of the point which divides the line segment joining the points P (– 2, 3, 5) and Q (1, – 4, 6) in the ratio 2 : 3 externally is given by:

Hence, the coordinates of the point which divides the line segment joining the points (-2, 3, 5) and (1, -4, 6) is (-8, 17, 3).

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