find the smallest sphere which touches the lines (x-2)/1=(y-1)/-2=(z-6)/1 and (x+3)/7=(y+3)/-6=(z+3)/1
1
Expert's answer
2020-09-20T17:51:37-0400
Solution
We will first find the distance between the two lines. Then that is the diameter of smallest sphere touching the two st. lines. Dividing the diameter by 2 we will get the radius of the sphere.
The two lines L1 and L2 are
<t1−2,2−2t1,t1−6>and<7t2+21,−6t2−18,t2+3>
The vector P between the two touchpoints P1 and P2must be perpendicular to both direction vectors of the lines L1andL2
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