Find parametric equations of the line through (1, 2, 5) that is perpendicular to

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Let the parametric equation of the line be x=1+t y=2+at z=5+bt Since the lines are perpendicular m1.m2=0 =>(i+aj+bk).(i-j+k)=0 =>1-a+b=0 =>a-b=1 The equation of second line in parametric form is x=m+1 y=m-1 z=m Since they intersect m+1=1+t => m=1 m-1=2+at =>t(1-a)=3 m=5+bt =>t(1-b)5 dividing 2nd and 3rd equation (1-a)/(1-b)=3/5 =>3-3a=5-5b => 3a - 5b=-2 Hence not we got 2equations and 2 variables 3a - 5b=-2 a-b=1 Whoese solutions are a=7/2, b=5/2 Hence the parametric equations are x=1+t y=2+7t/2 z=5+5t/2 or x=1+2t y=2+7t z=5+5t

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