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

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 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)

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

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

Expand : (i) (3x - 4y +5z)^2

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

Solve the equations by matrix method : (i) x+2y+z=7 x+2y+z=7 x+3z=11

The image of the line (x-1)/3=(y-3)/1=(z-4)/(-5) in the plane 2x-y+z+3=0 is the line (1) (x+3)/3=(y-5)/1=(z-2)/(-5) (2) (x+3)/(-3)=(y-5)/(-1)=(z+2)/5 (3) (x-3)/3=(y+5)/1=(z-2)/(-5) (3) (x-3)/(-3)=(y+5)/(-1)=(z-2)/5