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`

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"\ 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 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

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)

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

The equation of the line intersection of the planes 4x+4y-5z=12 and 8x+12y-13z=32 can be written as: (A) x/2=(y-1)/3=(z-2)/4 (B) x/2=y/3=(z-2)/4 (C) (x-1)/2=(y-2)/3=z/4 (D) (x-1)/2=(y-2)/(-3)=z/4

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

Find the product: (3x-4y+5z)\ (9x^2+16 y^2+25 z^2+12 x y-15 z x+20 y z)