Statement 1 : Lines `vecr=hati+hatj-hatk+lamda(3hati-hatj) and vecr=4hati-hatk+ mu (2hati+ 3hatk) intersect. Statement 2 : If `vecbxxvecd=vec0`, then
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.
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.
1 Answers
Correct Answer - 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.