find the distance of (1 0 0) from the line r=t(12i-3j-4k)
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5/13 is the distance
let the point A[1,0,0]
and the point on the given line be P[12t,-3t,-4t]
direction ratio of PA :[1-12t,3t,4t]
for PA to be perpendicular to the given line, the dot product of PA and the line is 0.
==> [1-12t,3t,4t].[12,-3,-4]=0
==>12-144t-9t-16t = 0
==> t = 12/169
so point P is [144/169,-39/169,-48/169]
distance AP = √{[1-144/169]^2+[36/169]^2+[48/169]^2}= 5/13 units
so the answer is 5/13
hope this helps
let the point A[1,0,0]
and the point on the given line be P[12t,-3t,-4t]
direction ratio of PA :[1-12t,3t,4t]
for PA to be perpendicular to the given line, the dot product of PA and the line is 0.
==> [1-12t,3t,4t].[12,-3,-4]=0
==>12-144t-9t-16t = 0
==> t = 12/169
so point P is [144/169,-39/169,-48/169]
distance AP = √{[1-144/169]^2+[36/169]^2+[48/169]^2}= 5/13 units
so the answer is 5/13
hope this helps
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