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Home » Find the ratio in which the point C(5, 9, -14) divides the join of A(2, -3, 4) and B(3, 1, -2).
Find the ratio in which the point C(5, 9, -14) divides the join of A(2, -3, 4) and B(3, 1, -2).
CBSE | Class 11 | Exercise 26C | Maths | RS Aggarwal | Three Dimensional Geometry
Find the ratio in which the point C(5, 9, -14) divides the join of A(2, -3, 4) and B(3, 1, -2).

Answer:

Let the ratio be k:1 in which point R divides point P and point Q, where  m and n are k and 1.

The point which this formula gives is already given.

R(5,9,-14) and the joining points are P(2, -3, 4) and Q(3, 1, -2).

Formula –

Using the above formula,

\begin{array}{l} (5, 9, -14) = \left( {\frac{{k \times 3 + 1 \times 2}}{{k + 1}},\frac{{k \times 1 + 1 \times -3}}{{k + 1}},\frac{{k \times -2 + 1 \times 4}}{{k + 1}}} \right)\\ 5 = {\frac{{k \times 3 + 1 \times 2}}{{k + 1}} \end{array}

5k + 5 = 3k + 2

2k = -3

k = -3/2

The ratio is -3:2. hence the division is external division.

The external division ratio is 3:2.

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