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Class 12

Shortest Distance Between Lines, with Mixed Practice — Quiz

Five questions on the shortest distance between skew and parallel lines. Pick one answer for each.

5 questions, one mark each. 3 to pass. Suggested time: 10 minutes. Your answers are not recorded.

  1. Two lines in space that are neither parallel nor intersecting are called
  2. Find the shortest distance between r⃗=i^+λj^\vec r = \hat i + \lambda\hat j and r⃗=3k^+μi^\vec r = 3\hat k + \mu\hat i.
  3. Find the distance between the parallel lines r⃗=λ(2i^−j^+2k^)\vec r = \lambda(2\hat i - \hat j + 2\hat k) and r⃗=3j^+μ(2i^−j^+2k^)\vec r = 3\hat j + \mu(2\hat i - \hat j + 2\hat k).
  4. If the shortest distance between two non-parallel lines is 00, the lines
  5. In the formula d=∣(b⃗1×b⃗2)⋅(a⃗2−a⃗1)∣b⃗1×b⃗2∣∣\displaystyle d = \left\lvert\dfrac{(\vec b_1 \times \vec b_2) \cdot (\vec a_2 - \vec a_1)}{\lvert\vec b_1 \times \vec b_2\rvert}\right\rvert, the vector b⃗1×b⃗2\vec b_1 \times \vec b_2 is
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