InterviewSolution
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InterviewSolution
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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. |
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Answer» 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. |
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