IB-06three_di_geometry(25-28)

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Powered by www.myengg.com THREE DIMENSIONAL GEOMETRY PREVIOUS EAMCET BITS 1. The perimeter of the triangle with vertices at (1, 0, 0), (0, 1, 0) and (0, 0, 1) is [EAMCET 2009] 1) 3 Ans: 4 2) 2 3) 2 2 4) 3 2 Sol. AB = BC = CA = 2 2. Sol. ∴ Perimeter = 3 2 In ΔABC the midpoints of the sides AB, BC and CA are respectively (l, 0, 0), (0, m, 0) and (0, 0, AB2 + BC2 + CA 2 n). Then [EAMCET 2008] A2 + m2 + n 2 1) 2 2) 4 3) 8 4) 16 Ans: 3 ( A, 0, 0 )( 0, m, 0 )( 0, 0, n ) are the midpoint of AB
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   1 THREE DIMENSIONAL GEOMETRY PREVIOUS EAMCET BITS 1. The perimeter of the triangle with vertices at (1, 0, 0), (0, 1, 0) and (0, 0, 1) is [EAMCET 2009] 1) 3 2) 2 3) 22 4) 32  Ans: 4Sol. ABBCCA2 ===  Perimeter32 ∴=  2. In Δ ABC the midpoints of the sides AB, BC and CA are respectively ( l , 0, 0), (0, m, 0) and (0, 0,n). Then 222222 ABBCCAmn ++++    [EAMCET 2008] 1) 2 2) 4 3) 8 4) 16Ans: 3Sol. ( )( )( ) ,0,00,m,00,0,n  are the midpoint of AB, BC, CA ( ) ( ) ( ) A,m,n,B,m,n,C,m,n ⇒=−=−=−      ( ) ( ) ( ) ( ) ( ) ( ) 222222222 ABBCCAmmnnmmnn ++=−+−−+++++−+−−       ( ) ( ) ( ) 22222222 mmnn04m4n04n44m0 +−−+++−=+++++++      ( ) 222222 88m8n8mn =++=++     222222 ABBCCA8mn ++⇒=++   3. The ratio in which yz-plane divides the line segment joining (–3, 4, –2), (2, 1, 3) is [EAMCET 2007] 1) – 4 : 1 2) 3 : 2 3) –2 : 3 4) 1 : 4Ans: 2Sol. 12 x:x3:2 −=  4. If OA is equally inclined to OX, OY and OZ and If A is 3 units from the srcin, then A is [EAMCET 2006] 1) (3, 3, 3) 2) (–1, 1, –1) 3) (–1, 1, 1) 4) (1, 1, 1)Ans: 4Sol. α = β = γ 1coscoscos3 α=β=γ=± OA3 =  ( ) AOAcos,OAcos,OAcos =αβγ  Powered by www.myengg.comPowered by www.myengg.com  Three Dimensional Geometry 2 ( )( ) ( ) 1,1,11,1,1or1,1,1 =±±±=−−−  5. The point collinear with (1, –2, –3) and (2, 0, 0) among the following is [EAMCET 2005] 1) (0, 4, 6) 2) (0, –4, –5) 3) (0, –4, –6) 4) (0, –4, 6)Ans: 3Sol. Three points are collinearif  121212232323 xxyyzzxxyyzz −−−==−−− verification6. XOZ plane divides the join of (2, 3, 1) and (6, 7, 1) in the ratio : [EAMCET 2003] 1) 3 : 7 2) 2 : 7 3) –3 : 7 4) –2 : 7Ans: 3Sol. 12 y:y3:7 −=−  7. If the plane7x11y13z3003 ++= meets the coordinate axes in A, B, C then the centroid of the Δ ABC is [EAMCET 2002] 1) ( ) 143,94,772) ( ) 143,77,913) ( ) 91,143,774) ( ) 143,66,91 Ans: 1Sol. ( ) A429,0,0  ( )( ) le B0,282,0C0,0,231areverticesofABC Δ  then centroid is ( ) 111 xyz,,143,94,77333 ∑∑∑⎛⎞=⎜⎟⎝⎠  8. If the extremities of a diagonal of a square are (1, –2, 3), (2, –3, 5) then the length of its side is [EAMCET 2001] 1) 6 2) 3 3) 5 4) 7Ans: 2Sol. Length of the diagonal = 6 ∴ Length of the side =d32 =            Powered by www.myengg.comPowered by www.myengg.com
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