Q. 1

Name the octants in which the following points lie:

(i) (5, 2, 3)

(ii) (-5, 4, 3)

(iii) (4, -3, 5)

(iv) (7, 4, -3)

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

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

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

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

Answer :

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’


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