19.1	a) 8*6*cos (2*pi/3)
	b) (2^2+3^2-4^2)/2
	c) (4^2+12^2-10^2)/2
	f) 3*1*cos(0)

19.2	a) (2,-3).(4,2)
	b) (2,-3,1).(4,2,-5)
	c) (7,-4,2).(3,1,0)
	d) (0,0,0).(-2,6,0)

19.4	sqrt(4^2+2^2+6^2+2*(2*4+2*6+4*6)*cos(pi/3))

19.5	x+3y-14=0

19.6	18*x-8y-53=0

19.9	a) 6-4 = sqrt(10)*sqrt(20)*cos(alpha)
	c) 2-4-4 = sqrt(9)*sqrt(21)*cos(alpha)

19.10	a) arccos((2,-7).(5,2)/sqrt(((2,-7).(2,-7))*((5,2).(5,2))))
	b) arccos((4,16,-12).(-6,-24,18)/sqrt(((4,16,-12).(4,16,-12))*((-6,-24,18).(-6,-24,18))))
	c) arccos((2,1,-8).(7,2,2)/sqrt(((2,1,-8).(2,1,-8))*((7,2,2).(7,2,2))))
	d) arccos((5,-3,2).(1,3,4)/sqrt(((5,-3,2).(5,-3,2))*((1,3,4).(1,3,4))))

19.11	a) (2,-5).(3,4)/sqrt((3,4).(3,4)) * b/sqrt((3,4).(3,4))
	b) (4,-5,7).(-3,-2,4)/sqrt((-3,-2,4).(-3,-2,4)) * b/sqrt((-3,-2,4).(-3,-2,4))

19.13	arccos((3,0,4).(7,0,1)/sqrt(((3,0,4).(3,0,4))*((7,0,1).(7,0,1))))

19.14	arccos((1,1,0).(1,1,1)/sqrt(((1,1,0).(1,1,0))*((1,1,1).(1,1,1))))

19.16	a) 3*4*sin(pi/3)
	b) 5*7*sin(arccos(-21/(5*7)))
	c) 3*6*sin(pi)
	d) a*b*sin(k*pi)

19.17	CrossProduct[(2,-3,1),(5,1,-2)], CrossProduct[(0,0,0),(2,-3,1)], CrossProduct[3(2,-3,1)-2(5,1,-2),(2,-3,1)+5(5,1,-2)]

19.19	b) CrossProduct[(1,-3,2),(-3,-1,-4)].CrossProduct[(1,-3,2),(-3,-1,-4)]
	d) CrossProduct[{3,-3,0},{-2,-1,0}].CrossProduct[{3,-3,0},{-2,-1,0}]

19.21	:(

19.25	a) Det[{-3,4,-7},{1,2,5},{1,-4,5}]
	c) -2*4*sin(pi/2)/3*3^2

19.26	Det[{3,6,3},{1,3,-2},{2,2,2}]
	CrossProduct[{3,6,3},{1,3,-2}].CrossProduct[{3,6,3},{1,3,-2}]
	(18/6)/((1/2)*sqrt(531)/3)

19.28	Det[{-1,-1,6},{-2,0,2},{1,-1,4}]