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Question
If θ is the angle between the lines whose vector equations are →r=3→i+2→j+4→k+λ(→i+2→j+2→k) and →r=5→i−2→k+μ(3→i+2→j+6→k); λ and μ being parameters, then
If θ is the angle between the lines whose vector equations are →r=3→i+2→j+4→k+λ(→i+2→j+2→k) and →r=5→i−2→k+μ(3→i+2→j+6→k); λ and μ being parameters, then
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Solution
The correct options are
A cosθ=1921
C sinθ=4√521
The angle between lines →r=3→i+2→j+4→k+λ(→i+2→j+2→k) and →r=5→i−2→k+μ(3→i+2→j+6→k) is
θ=cos−1⎡⎢
⎢⎣(^i+2^j+^2k).(3^i+2^j+6^k)√(12+22+22)(32+22+62)⎤⎥
⎥⎦=cos−1(1921)
⇒sinθ=√1−cos2θ=4√521
⇒θ=sin−1(4√521)
Ans: A,C
A cosθ=1921
C sinθ=4√521
The angle between lines →r=3→i+2→j+4→k+λ(→i+2→j+2→k) and →r=5→i−2→k+μ(3→i+2→j+6→k) is
θ=cos−1⎡⎢ ⎢⎣(^i+2^j+^2k).(3^i+2^j+6^k)√(12+22+22)(32+22+62)⎤⎥ ⎥⎦=cos−1(1921)
⇒sinθ=√1−cos2θ=4√521
⇒θ=sin−1(4√521)
Ans: A,C
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