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Question
The reflection of the point A(1,0,0) in the line x−12=y+1−3=z+108 is:
The reflection of the point A(1,0,0) in the line x−12=y+1−3=z+108 is:
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Solution
The correct option is B (5,−8,−4)
Let x−12=y+1−3=z+108=r
Any point P on the line is (2r+1,−3r−1,8r−10)
D.r's of AP are (2r,−3r−1,8r−10)
AP is perpendicular to the given line with DR's (2,−3,8)
2(2r)−3(−3r−1)+8(8r−10)=0⇒r=1∴P(3,−4,−2)
Reflection and object will be equidistant from line and vectors joining them will be equal.
Let B(x,y,z) be the image of A
∴(x−3)^i+(y+4)^j+(z+2)^k=(3−1)^i+(−4−0)^j+(−2−0)^k
Thusx−3=2,x=5
Thusy+4=−4,y=−8
Thusz+2=−2,z=−4
Required reflection point is B=(5,−8,−4)
Let x−12=y+1−3=z+108=r
Any point P on the line is (2r+1,−3r−1,8r−10)
D.r's of AP are (2r,−3r−1,8r−10)
AP is perpendicular to the given line with DR's (2,−3,8)
2(2r)−3(−3r−1)+8(8r−10)=0⇒r=1∴P(3,−4,−2)
Reflection and object will be equidistant from line and vectors joining them will be equal.
Let B(x,y,z) be the image of A
∴(x−3)^i+(y+4)^j+(z+2)^k=(3−1)^i+(−4−0)^j+(−2−0)^k
Thusx−3=2,x=5
Thusy+4=−4,y=−8
Thusz+2=−2,z=−4
Required reflection point is B=(5,−8,−4)
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