InterviewSolution
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InterviewSolution
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Statement 1: Distance of point D( 1,0,-1) from the plane of points A( 1,-2,0) , B ( 3, 1,2) and C( -1,1,-1) is `8/sqrt229` Statement 2: volume of tetrahedron formed by the points A,B, C and D is `sqrt229/ 2`A. Both the statements are true and statement 2 is the correct explanation for statement 1.B. Both statements are true but statement 2 is not the correct explanation for statement 1.C. Statement 1 is true and Statement 2 is falseD. Statement 1 is false and Statement 2 is true. |
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Answer» Correct Answer - d `vec(AD)=2hatj -hatk ,vec(BD) =-2hati -hatj -3hatk and vec(CD)=2hati-hatj` volume of tetrahedron = `1/6 [vec(AD) vec(BD) vec(CD)]` `=1/6||{:(0,2,-1),(-2,-1,-3),(2,-1,0):}||=8/3` Also, area of the triangle ABC = `1/2 |vec(AB) xx vec(AC)|` `1/2||{:(hati,hatj,hatk),(2,3,2),(-2,3,-1):}||` ` 1/2 |-9hati - 2hatj +12 hatk|` `sqrt229/2` Then ` 8/3 = 1/3 xx` (Distance of D from base ABC) `xx` (Area of triangle ABC) Distance of D from base ABC` = 16//sqrt229` |
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