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Find the radius of the circular sectio...

Find the radius of the circular section in which the sphere `| vec r|=5` is cut by the plane ` vecr*( hat i+ hat j+ hat k)=3sqrt(3.)`

Text Solution

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Let `A` be the foot of the perpendicular from the centre O to the plane
`" "vecr*(hati+hatj+hatk)-3sqrt(3)=0`
Then `" "|OA|=|(0*(hati+hatj+hatk)-3sqrt(3))/(|hati+hatj+hatk|)|=(3sqrt3)/(sqrt3)=3`
`" "` (Perpendicular distance of a point from the plane)
If P is any point on the circle, then P lies on the plane as well as on the sphere. Therefore,
`" "OP=` Radius of the sphere = 5
Now `" "AP^(2)=OP^(2)-OA^(2)=5^(2)-3^(2)=16 or AP=4`
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