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Question 183 of 215

Q.Using vector method, find incentre of the triangle whose vertices are P(0,4,0)P(0, 4, 0), Q(0,0,3)Q(0, 0, 3) and R(0,4,3)R(0, 4, 3).

Maharashtra MsbshseMaharashtra HSC (MSBSHSE) Board 2017Subjective· 4mImportance★★★★★
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Compute side lengths (opposite each vertex), then use the weighted incentre formula pP⃗+qQ⃗+rR⃗p+q+r\dfrac{p\vec P+q\vec Q+r\vec R}{p+q+r}.

P(0,4,0)P(0,4,0), Q(0,0,3)Q(0,0,3), R(0,4,3)R(0,4,3).

Side opposite PP is QRQR: length p=∣QR∣=(0−0)2+(4−0)2+(3−3)2=16=4p = |QR| = \sqrt{(0-0)^2+(4-0)^2+(3-3)^2} = \sqrt{16} = 4

Side opposite QQ is PRPR: length q=∣PR∣=(0−0)2+(4−4)2+(3−0)2=9=3q = |PR| = \sqrt{(0-0)^2+(4-4)^2+(3-0)^2} = \sqrt{9} = 3

Side opposite RR is PQPQ: length r=∣PQ∣=(0−0)2+(0−4)2+(3−0)2=16+9=5r = |PQ| = \sqrt{(0-0)^2+(0-4)^2+(3-0)^2} = \sqrt{16+9} = 5

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