Question

10. Write an equation for the plane containig the points (-7,2,1). (9.0,-2) and (-5, -1,2). Is this plane parallel, perpendicular or neither to the plane 2x - 3y + 2 = 5? 11. Consider the line that passes through the point (6, -5,2) and that is parallel to the vector (-1, 1, 3). (a) Find symmetric equations for this line (b) Find the point at which this line passes through the yz-plane.

Answer 1

vecter the three equation points of a blossp anning through with position vector a lt a). 10-a) x60-a)]=0 a= (-7,2,1) 5 = 29,0,-2) zo (-5,-1,2) 1-2-97-3C 16+6) (-48+4) (5-2) x (E-2) = -11 ? - 22 7 - 444 cs-a) - 2 + 3 + ... + 5 1) = 4+2) û +(y-2) I +(2-1) 2 ). [-a)x(-a'] [(+7) 2 + € 4+2) } +(2-182] [-12 - 229 -4 th) = - 11 (n+7) 22 (4.2) 44 (2-1) = -11 [(x + 7) +2 (4-2) + 4(2-1)]=0 4+7+ 24-4+42-4=u +24+42-1=0 - 0 This is the required eqreof plase We given 20-34+2-550 - aig thibe + 16 = 2 6 + 4 = 6-6=0 - plase o & blaue as t.

- 1 ras ega of the line paning through (6,-5,2) and il to the vector (-2,2,3) 9 %-6 Skts92 = This is synretic eqr of lese chy : eine passes through yr-plane 0-6 = 1 = [6=6) .: 9= 6-5=1, 2 = 3x6 + 2 = 20 Poists are (2,4, 2) = (0, 1,20).