Find the angle between the following lines and the planes : (i) line `vecr=(hati+2hatj-hatk)+lambda(hati-hatj+hatk)` and planes `vecr.(2hati-hatj+hatk
Find the angle between the following lines and the planes :
(i) line `vecr=(hati+2hatj-hatk)+lambda(hati-hatj+hatk)` and planes `vecr.(2hati-hatj+hatk) = 4`.
(ii) line `vecr = (2hati+3hatj+9hatk)+lambda(2hati+3hatj+4hatk)` and plane `vecr.(hati+hatj+hatk) =5`.
(iii) line `(x+1)/(3) = y/2 = z/4` and plane `2x+y-3z=5`.
(iv) line `(x-3)/(9) = (y+4)/(6) = (z+2)/(2)` and plane `3x-y+z=0`.
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Correct Answer - (i) `sin^(-1)((2sqrt(2))/(3))`, (ii) `sin^(-1)((3sqrt(3))/(sqrt(29)))`, (iii) `sin^(-1)((-4)/(sqrt(406)))` , (iv) `sin^(-1)((23)/(11sqrt(11)))`
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