3D Geometry 3 Question 15

15. If an angle between the line, x+12=y21=z32 and the plane,

(2019 Main, 12 Jan II) x2ykz=3 is cos1223, then value of k is

(a) 53

(b) 35

(c) 35

(d) 53

Show Answer

Answer:

(a)

Solution:

  1. Clearly, direction ratios of given line are

2,1,2 and direction ratios of normal to the given plane are 1,2,k.

As we know angle ’ θ ’ between line and plane can be obtained by

sinθ=|a1a2+b1b2+c1c2|a12+b12+c12a22+b22+c22 So, sinθ=|22+2k|4+1+41+4+k2sincos1223=|2k|35+k2 given θ=cos12232|k|35+k2=13cosθ=223sinθ=13θ=sin113cos1223=sin113Δ34k2=5+k23k2=5k=±53



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