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3D Geometry question

2019 · Shift 1 · Q27
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  2. /JEE Advanced
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  5. /2019 · Shift 1 · Q27

3D Geometry question

2019 · Shift 1 · Q27

JEE AdvancedMathematics3D GeometryMultiple correct+4 / −1
Let L1 and L2 denote the lines r=i^+λ(−i^+2j^+2k^)r = \widehat i + \lambda ( - \widehat i + 2\widehat j + 2\widehat k)r=i+λ(−i+2j​+2k), λ∈\lambda \inλ∈ R and r=μ(2i^−j^+2k^), μ∈Rr = \mu (2\widehat i - \widehat j + 2\widehat k),\,\mu \in Rr=μ(2i−j​+2k),μ∈R respectively. If L3 is a line which is perpendicular to both L1 and L2 and cuts both of them, then which of the following options describe(s) L3?
  1. A
    r=29(2i^−j^+2k^)+t(2i^+2j^−k^), t∈Rr = {2 \over 9}(2\widehat i - \widehat j + 2\widehat k) + t(2\widehat i + 2\widehat j - \widehat k),\,t \in Rr=92​(2i−j​+2k)+t(2i+2j​−k),t∈R
  2. B
    r=13(2i^+k)+t(2i^+2j^−k^), t∈Rr = {1 \over 3}(2\widehat i + k) + t(2\widehat i + 2\widehat j - \widehat k),\,t \in Rr=31​(2i+k)+t(2i+2j​−k),t∈R
  3. C
    r=29(4i^+j^+k^)+t(2i^+2j^−k^), t∈Rr = {2 \over 9}(4\widehat i + \widehat j + \widehat k) + t(2\widehat i + 2\widehat j - \widehat k),\,t \in Rr=92​(4i+j​+k)+t(2i+2j​−k),t∈R
  4. D
    r = t(2i^+2j^−k^)t(2\widehat i + 2\widehat j - \widehat k)t(2i+2j​−k), t∈Rt \in Rt∈R
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