1. Tardigrade
  2. Question
  3. Mathematics
  4. The vector equations of two lines L1 and L2 are respectively vec r =17 hat i -9 hat j +9 hat k +λ(3 hat i + hat j +5 hat k ) and vec r =15 hat i -8 hat j - hat k +μ(4 hat i +3 hat j ) I L 1 and L 2 are skew lines II (11,-11,-1) is the point of intersection of L 1 and L 2 III (-11,11,1) is the point of intersection of L 1 and L 2 IV cos -1(3 / √35) is the acute angle between L1 and L2 then, which of the following is true?

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Q. The vector equations of two lines $L_{1}$ and $L_{2}$ are respectively
$\vec{ r }=17 \hat{ i }-9 \hat{ j }+9 \hat{ k }+\lambda(3 \hat{ i }+\hat{ j }+5 \hat{ k })$ and $\vec{ r }=15 \hat{ i }-8 \hat{ j }-\hat{ k }+\mu(4 \hat{ i }+3 \hat{ j })$
I $L _{1}$ and $L _{2}$ are skew lines
II $(11,-11,-1)$ is the point of intersection of $L _{1}$ and $L _{2}$
III $(-11,11,1)$ is the point of intersection of $L _{1}$ and $L _{2}$
IV $\cos ^{-1}(3 / \sqrt{35})$ is the acute angle between $L_{1}$ and $L_{2}$
then, which of the following is true?

Vector Algebra

Solution:

Correct answer is (a) II and IV