Q. 205.0( 1 Vote )

Find the value of

Answer :

Formula: -


(i)in Cartesian form of the lines



And


(ii) Two line with direction ratio and are perpendicular if then


Given: -


And



Arranging the above


and



Arranging the above equation as in form of


And



So, the Cartesian form is


Where x1 = 5, x2 = 0, y1 = 2, y2 = - �, z1 = 1,z2 = 1,


a1 = 5λ+2, a2 = 1, b1 = -5, b2 = 2λ,c1 = 1,c2 = 3


The direction ratio of these lines are and5λ+2, -5,1 and 1, 2λ ,3


Since the line are perpendicular


Then using formula (ii)


a1a2 + b1b2 +c1c2 = 0


(5λ+2)(1)+(-5)(2λ)+1(3) = 0


5λ+2-10λ+3 = 0


-5λ = -5


λ = 1


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