Verity the property: `x\ "x"\ (y+z)=x\ "x"\ y+x\ "x"\ z\ , \ `(i )x=(-8)/3, y=5/6, z=(-13)/(12)` (ii) `x=(-3)/4, y=(-5)/2, z=7/6`

Verity the property: x\ "x"\ (y+z)=x\ "x"\ y+x\ "x"\ z\ :\ (i) x=(-3)/7, y=(12)/(13), z=(-5)/6 (ii) x=(-12)/5, y=(-15)/4, z=8/3

Verify the property: x\ "x"\ (y" x" z)=(x\ "x "y)"x"\ z\ b y\ taking:\ (i) x=7/3, y=(12)/5, z=4/9 (ii) x=0, y=(-3)/5, z=(-9)/4

Verity the property: x\ "x"\ (y"\ x"\ z)=(x\ "x \ "y)x\ z\ x=1/2, y=5/(-4), z=(-7)/5 x=5/7, y=(-12)/(13), z=(-7)/(18)

Verify that x xx(y-z)=x xxy-x xxz , if (i) x=(4)/(5), y=-(7)/(4) "and" z=3 (ii) x=(3)/(4), y=(8)/(9) "and" z=-5

Verify that (x+y)xxz=x xxz+yxxz , if (i) x=(4)/(5), y=(-2)/(3) "and" z=-4 (ii) x=2, y=(4)/(5) "and" z=(3)/(-10)

Verify associativity of addition of rational i.e., (x+y)+z=x+(y+z), when: (i ) x=1/2, y=2/3,\ z=-1/5 (ii) x=(-2)/5, y=4/3,\ z=\ (-7)/(10)

Find the product: (3x+2y+2z)\ \ (9x^2+4y^2+\ 4\ z^2-\ 6\ x y-4\ y z-6z x)

Verify associativity of addition of rational i.e., (x+y)+z=x+(y+z), when: x=\ (-7)/(11), y=2/(-5),\ z=\ (-3)/(22) (ii) x=-2, y=3/5,\ z=\ (-4)/3

Perpendiculars are drawn from points on the line (x+2)/2=(y+1)/(-1)=z/3 to the plane x + y + z=3 The feet of perpendiculars lie on the line (a) x/5=(y-1)/8=(z-2)/(-13) (b) x/2=(y-1)/3=(z-2)/(-5) (c) x/4=(y-1)/3=(z-2)/(-7) (d) x/2=(y-1)/(-7)=(z-2)/5

Add the following: (i) x – 3y – 2z , 5x + 7y – 8z , 3x – 2y + 5z