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Question

A line passes through two points A(2, 3, 1) and B(8, 1, 2). The coordinates of a point on this line at a distance of 14 units from A are

A
(14, 1, 5)
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B
(10, 7, 7)
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C
(86, 25, 41)
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D
(0, 0, 0)
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Solution

The correct option is A (14, 1, 5)
Equation of line passing through two points
xx1x2x1=yy1y2y1=zz1z2z1=λ

x282=y(3)1(3)=z(1)z(1)=λ

x=6λ+2

y=2λ3

z=3λ1

Distance between A and general point of line
(6λ+22)2+(2λ3+3)2+(3λ1+1)2=142

36λ2+4λ2+9λ2=142

49λ2=196

λ2=4

λ=±2

x=14, y=1 and z=5
Or,
x10, y=7 and z=7

So, The coordinates of point =(14,1,5)
Hence. the option (A) is the correct answer.

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