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Question

Assertion :If the lines x−x1a1=y−y1b1=z−z1c1 and x−x2a2=y−y2b2=z−z2c2 are coplanar then ∣∣ ∣∣x1y1z1a1b1c1a2b2c2∣∣ ∣∣=∣∣ ∣∣x2y2z2a1b1c1a2b1c1∣∣ ∣∣



Reason: If two lines are coplanar then shortest distance between them is zero

A
Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
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B
Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
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C
Assertion is correct but Reason is incorrect
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D
Assertion is incorrect but Reason is correct
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Solution

The correct option is C Assertion is correct but Reason is incorrect
If two lines xx1a1=yy1b1=zz1c1 and xx2a2=yy2b2=zz2c2 are coplanar then

∣ ∣x1y1z1a1b1c1a2b2c2∣ ∣=∣ ∣x2y2z2a1b1c1a2b2c2∣ ∣

Therefore assertion is correct

Two lines are coplanar means , they should lie on same plane , shortest distance need not be zero

For example take two parallel lines which lie on same plane , the shortest distance between them is not zero

Therefore reason is false

So the correct option is C

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