aba = 5, 1, 6 b = 1, 0, 3 ab = 3, 21, 1 ab = 1, 1, 9 ab = 6, 5, 1 ab = 3 ...

Name: __________________ Class: Date: _____________11 Find a vector equation and parametric equations for the linethrough the point ( 7, 0, 10 ) and perpendicular to the plane9x + 7y + 8z = 8 .r = ( 6 + 11t ) i + 9t j + ( 9 + 10t ) k ;a.x = 6 + 11t , y = 9t , z = 9 + 10tr = ( 9 + 12t ) i + 10t j + ( 12 + 11t ) k ;b.x = 9 + 12t , y = 10t , z = 12 + 11tr = ( 10 + 13t ) i + 11t j + ( 13 + 12t ) kc. ; x = 10 + 13t , y = 11t , z = 13 + 12tr = ( 7 + 9t ) i + 7t j + ( 10 + 8t ) k ;d.x = 7 + 9t , y = 7t , z = 10 + 8t13 Find parametric equations and symmetric equations for the lineof intersection of the planes 3x + 4y + 6z = 4 and3x + 4z = 0 . x = 19t , y = 1 + 9t , z = 15t ;a. x19 = y 1 =z9 15 x = 16t , y = 1 + 6t , z = 12t ;b. x16 = y 1 =z6 12 x = 20t , y = 1 + 10t , z = 16t ;c. x20 = y 1 =z10 16r = ( 11 + 8t ) i + 6t j + ( 14 + 7t ) k ;e.x = 11 + 8t , y = 6t , z = 14 + 7t x = 14t , y = 1 + 4t , z = 10td. x14 = y 1 =z4 10;12 Find parametric equations and symmetric equations for the linethrough the points ( 15, 8, 8 ) and ( 8, 14, 7 ) .x = 16 8t , y = 9 + 7t , z = 9 +a.16tx 16; = y 9 = z + 9 8 7 16x = 11 3t , y = 4 + 2t , z = 4 +b.11tx 18; = y 4 = z + 4 3 2 11 x = 17t , y = 1 + 7t , z = 13t ;e. x17 = y 1 =z7 1314 Which of the following pairs of points lies on a line that isparallel to the line through points ( 2, 1, 2 ) and( 5, 2, 4 ) ?a.( 8, 5, 7 ), ( 11, 6, 9 )x = 13 5t , y = 6 + 4t , z = 6 +c.13tx 13; = y 6 = z + 6 5 4 13b.c.( 12, 9, 11 ), ( 12, 7, 10 )( 9, 6, 8 ), ( 9, 4, 7 )x = 15 7t , y = 8 + 6t , z = 8 +d.15tx 15; = y 8 = z + 8 7 6 15x = 18 10t , y = 11 + 9t , z = 11 + 18tx 18; = y 11 =e. 10 9z + 1118d.e.( 5, 2, 4 ), ( 15, 10, 13 )( 6, 3, 5 ), ( 8, 3, 6 )15 In what points does the line through ( 7, 3, 0 ) that isperpendicular to the plane 4x y + z = 1 intersectthe coordinate planes?PAGE 3

Name: __________________ Class: Date: _____________16 Find an equation of the plane through the pointand with normal vector 5 j + 9k .( 2, 0, 2 )20 Which of the following planes is parallel to the plane4y + 9z = 4 ?5x 6y + 10z =5y + 9z = a. d.19184x + 8y +2x 5y +b. e.12z = 219z = 18c.7y 11z =2017 Find an equation of the plane through the points ( 0, 7, 2 ) ,( 2, 0, 2 ) , and ( 5, 7, 0 ) .16x + 4y 14x 4y +a. d.35z = 9335z = 9716x + 4y +15x 4y +b. e.35z = 10635z = 93c.14x + 4y +35z = 9818 Find an equation of the plane that passes through the point( 2, 6, 7 ) and contains the line x = 6t , y = 3 + t ,z = 5 t .10x 8y +25x + 20y a. d.7z = 345z = 310x + 8y +25x 20y +b. e.7z = 345z = 3c.45x 25y 20z =321 (a) Find symmetric equations for the line of intersection of theplanes x 4y + z = 9 and 4x + y + z = 9.(b) Find the angle between the planes.22 Find the distance from the point ( 3, 4, 3 ) to the plane8x 7y + z = 9 .23 Find the distance between the parallel planes 15x +15y 12z = 4 and 5x + 5y 4z = 8 .14x 5y +16x + 5y +a. d.16z = 3914z = 415x + 14y +14x 5y +b. e.16z = 3616z = 36c. 5x 14y +16z = 3819 Find the point at which the line x = 9 + 5t , y = 6t ,z = 14 7t intersects the plane x + 4y z + 5 = 0 .PAGE 4

Name: __________________ Class: Date: _____________ 24 Find the traces of the surface 7y = 3z 2 2x 2in theplanes x = k , y = k , and z = k . 26 Reduce the equation 9x y 2 + 9z 2 = 0 to one ofthe standard forms.x = k: 7y =y = k: 7y =3z 2 2k 2;3z 2 2k 2;y = k: 7k =z = k: 7k =a.3z 2 2x 2d.;3z 2 2x 2;z = k: 7y =x = k: 7y =3k 2 2x 2 3k 2 2x 2x = y 2+ z 2 y = x 2a. d.99x = y 218 z 2 x = y 2b. e.9 z 2 z 2x = k: 7y =x = k: 7y =3z 2 2k 2;3z 2 2k 2;z = k: 7k =y = k: 7k =b.3z 2 2x 2e.;3z 2 + 2x 2;y = k: 7y =z = k: 7y =3k 2 2x 2 3k 2 + 2x 2x = k: 7y =3z 2 + 2k 2;y = k: 7k =c.3z 2 + 2x 2;z = k: 7y =z = y 2c.9 x 227 Reduce the equation 6y 2 + z 2 x 96y 16z + 448 = 0 to one of the standard forms.a.b.x6 = ( y 8 ) 2 +x6 = ( y 8 ) 2 +( z 8 ) 26( z + 8 ) 263k 2 + 2x 225 Reduce the equation x 2 = 7y 2 + 9z 2to one of thestandard forms.x 263 = y 29a.z 2d.7x 263 = y 27z 29c.d.e.x8 = ( y 8 ) 2 +x6 = ( y 8 ) 2 x6 = ( y 8 ) 2 ( z 8 ) 28( z 8 ) 26( z + 8 ) 26x 2= y 29 63 +b.z 2e.7x 27z 263= y 29+c.x 263 = y 29z 27+PAGE 5

Name: __________________ Class: Date: _____________28 Reduce the equation x 2 y 2 + z 2 2x +2y + 10z + 22 = 0 to one of the standard forms.( x 1 ) 23a. ( y 1 ) 23+d.( z + 5 ) 23= 1 ( x 1 ) 23b. ( y + 1 ) 25+e.( z + 5 ) 23= 0( x + 1 ) 25( y 1 ) 23( z 5 ) 251( x 1 ) 23( y 5 ) 23( z + 5 ) 23=++= 130 Find an equation for the surface consisting of all points that areequidistant from the point ( 7, 0, 0 ) and the planex = 7 .7x = y 2 + z 2 7x 2 + y 2 +a. d.z 2 = 128x 2 + y 2 + 28x =b.z 2 e.= 0y 2 + z 228x 2 + y 2 +c.z 2 = 1c.( x + 5 ) 23( y 1 ) 23( z + 5 ) 23+= 029 Find an equation for the surface obtained by rotating the linex = 4y about the x axis.x 2a. d.16 + y 2 +z 2 = 1x 2 = y 2 +16z 2x 2b. e.y 216 = y 2 + z 2 z = 16x 2 x 2 + 4y 2 +c.16z 2 = 1PAGE 6