Given: Points are given

To find: name of the octant

Formula used:

Notation of octants:

If x, y and z all three are positive, then octant will be XOYZ

If x is negative and y and z are positive, then the octant will be X’OYZ

If y is negative and x and z are positive, then the octant will be XOY’Z

If z is negative and x and y are positive, then the octant will be XOYZ’

If x and y are negative and z is positive, then the octant will be X’OY’Z

If z and y are negative and x is positive, then the octant will be XOY’Z’

If x and z are negative and x is positive, then the octant will be X’OYZ’

If x, y and z all three are negative, then octant will be X’OY’Z’

(i) (5, 2, 3)

In this case, since x, y and z all three are positive then octant will be XOYZ

(ii) (-5, 4, 3)

In this case, since x is negative and y and z are positive then the octant will be X’OYZ

(iii) (4, -3, 5)

In this case, since y is negative and x and z are positive then the octant will be XOY’Z

(iv) (7, 4, -3)

In this case, since z is negative and x and y are positive then the octant will be XOYZ’

(v) (-5, -4, 7)

In this case, since x and y are negative and z is positive then the octant will be X’OY’Z

(vi) (-5, -3, -2)

In this case, since x, y and z all three are negative then octant will be X’OY’Z’

(vii) (2, -5, -7)

In this case, since z and y are negative and x is positive then the octant will be XOY’Z’

(viii) (-7, 2, -5)

In this case, since x and z are negative and x is positive then the octant will be X’OYZ’