1.

Statement 1 : Lines vecr=hati+hatj-hatk+lamda(3hati-hatj) and vecr=4hati-hatk+ mu (2hati+ 3hatk) intersect. Statement 2 : If vecbxxvecd=vec0, then lines vecr=veca+lamdavecb and vecr= vecc+lamdavecd do not intersect.

Answer»

Both the statements are true, andStatement 2 is the CORRECT explanation for Statement 1.
Both the Statements are true, but Statement 2 is not the correct explanation for Statement 1.
Statement 1 is true and Statement 2 is false.
Statement 1 is false and Statement 2 is true.

Solution :For the GIVEN lines, LET `vec(a_1) =hati+hatj-hatk, vec(a_2)= 4hati-hatk, vec(b_1) = 3hati-hatj and vec(b_2) = 2hati+3hatk`. Therefore,
`""[vec(a_(2))-vec(a_(1))vec(b_1)vec(b_2)]=|{:(4-1,,0-1,,-1+1),(3,,-1,,0),(2,,0,,3):}|`
`""= |{:(3,,-1,,0),(3,,-1,,0),(2,,0,,3):}|=0`
Hence, the lines are COPLANAR. Also VECTOR `vec(b_1) adn vec(b_2)`along which the lines are directed are not collinear.
Hence, the lines intersect. When `vecbxxvecd=vec0` , vectors and `vecr=vecc+lamdavecd` are parallel and do not intersect. But this statement is not the correct explanation for Statement 1.


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