09%20-%20Plane

09%20-%20Plane - PROBLEMS (1) 09 - PLANE Obtain the vector...

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PROBLEMS 09 - PLANE Page 1 ( 1 ) Obtain the vector and Cartesian equations of the plane through A ( 1, 2, 3 ), B ( 2, 1, 0 ) and C ( 3, 3, - 1 ). [ Ans: r = ( 1, 2, 3 ) + m ( 1, - 1, - 3 ) + n ( 2, 1, - 4 ), 7x - 2y + 3z = 12 ] ( 2 ) A plane intersects X-, Y- and Z-axes at A, B and C respectively. The centroid of triangle ABC is ( p, q, r ). Derive the equation of the plane. + + = 3 r z q y p x : Ans ( 3 ) Obtain the foot of perpendicular from the point ( 1, 2, 3 ) on the plane x - 2y + 2z = 5 and the distance of the point from the plane. 3 2 , 9 31 , 9 14 , 9 11 : Ans ( 4 ) Find the image of ( 1, 3, 4 ) relative to the plane 2x - y + z + 3 = 0. [ Ans: ( - 3, 5, 2 ) ] ( 5 ) Find the common section of x + 2y - 3z = 6 and 2x - y + z = 7. = = 5 z 7 1 y 1 4 x : Ans - - ( 6 ) Obtain the equation of the plane through ( 1, 3, 5 ) perpendicular to the intersection of 3x + y - z = 0 and x + 2y + 3z = 5. [ Ans:
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09%20-%20Plane - PROBLEMS (1) 09 - PLANE Obtain the vector...

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