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Statement 1: Lines vec r= hat i+ hat j-...

Statement 1: Lines ` vec r= hat i+ hat j- hat k+lambda(3 hat i- hat j)a n d vec r=4 hat i- hat k+mu(2 hat i+3 hat k)` intersect. Statement 2: ` vec bxx vec d=0` , then lines ` vec r= vec a+lambda vec ba n d vec r= vec c+lambda vec d` do not intersect.

A

Both the statements are true, and Statement 2 is the correct explanation for Statement 1.

B

Both the Statements are true, but Statement 2 is not the correct explanation for Statement 1.

C

Statement 1 is true and Statement 2 is false.

D

Statement 1 is false and Statement 2 is true.

Text Solution

Verified by Experts

The correct Answer is:
c
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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