The line equation is X = (1, 1, 3) + t(1, - 1, - 5).

i.e, (x, y, z) = (1, 1, 3) + t(1, - 1, - 5)

Solve the equations in terms of t.

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Rewrite this yields as :

, these are called symmetric equations for the given line.

To decide which of the points is lie on the line X = (1, 1, 3) + t(1, - 1, - 5), substitute each point in the symmetric equations.

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• Substitute the point (x, y, z) = (3, - 1, - 7) in equation (1).
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The above statement is true.

So, the point (2, - 1, 3) is lie on the line  X = (1, 1, 3) + t(1, - 1, - 5).

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• Substitute the point (x, y, z) = (- 2, 1, 3) in equation (1).
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The above statement is false.

So, the point (2, - 1, 3) is does not lie on the line  X = (1, 1, 3) + t(1, - 1, - 5).

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• Substitute the point (x, y, z) = (- 4, 6, 28) in equation (1).
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The above statement is true.

So, the point (- 4, 6, 28)  is lie on the line  X = (1, 1, 3) + t(1, - 1, - 5).

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• Substitute the point (x, y, z) = (2, 1, - 5) in equation (1).
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The above statement is false.

So, the point (2 , 1, - 5) is does not lie on the line  X = (1, 1, 3) + t(1, - 1, - 5).

Therefore, the points (- 4, 6, 28) and (2, - 1, 3) are lie on the line  X = (1, 1, 3) + t(1, - 1, - 5).