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If the line joining A(1,3,4) and B is divided by the point(−2,3,5) in the ratio 1:3, then B is

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(-11,3,8)

(-11,3,-8)

(-8,12,20)

(13,6,-13)

answer is A.

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Detailed Solution

We are given coordinates of point A as(1,3,4). Let us suppose coordinates of B a(x,y,z). We are also given coordinates of points which cut the line as(−2,3,5). Ratio is given as 1:3. Hence, by comparing with section formula,
Question Image

Putting in the formula, we get –

Comparing and separating the terms, we get –

Solving for value of x, we get –

Cross multiplying, we get –

Solving for value of y, we get –

Cross multiplying, we get –

Solving for value of z, we get –

Cross multiplying, we get –

From equation (1), (2) and (3), we get –

As we have supposed coordinates of B as(x,y,z). Therefore, the coordinates of B are(−11,3,8).
Hence, option (1) is the correct answer.

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If the line joining A(1,3,4) and B is divided by the point(−2,3,5) in the ratio 1:3, then B is

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