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Conditions for a system of linear equations to have a unique solution

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Question

Find the shortest distance between the lines whose vector equations are

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Solution

The given lines are

It is known that the shortest distance between the lines, and , is given by,

For the given equations,

Substituting all the values in equation (3), we obtain

Therefore, the shortest distance between the lines isunits.

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Conditions for a system of linear equations to have a unique solution

Standard XII Mathematics

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