Q. 1

# Find the distance between the points :

(i) A(5, 1, 2) and B(4, 6, -1)

(ii) P(1, -1, 3) and Q(2, 3, -5)

(iii) R(1, -3, 4) and S(4, -2, -3)

(iv) C(9, -12, -8) and the origin

Answer :

Formula:

The distance between two points (x_{1},y_{1},z_{1}) and (x_{2},y_{2},z_{2}) is given by

D=

(i) A(5, 1, 2) and B(4, 6, -1)

Here, (x_{1},y_{1},z_{1}) = (5, 1, 2)

(x_{2},y_{2},z_{2})= (4, 6, -1)

Therefore,

D =

=

=

=

Distance between points A and B is .

(ii) P(1, -1, 3) and Q(2, 3, -5)

Here, (x_{1},y_{1},z_{1})= (1, -1, 3)

(x_{2},y_{2},z_{2})= (2, 3, -5)

Therefore,

D =

=

=

= = 9

Distance between points P and Q are 9 units.

(iii) R(1, -3, 4) and S(4, -2, -3)

Here, (x_{1},y_{1},z_{1})= (1, -3, 4)

(x_{2},y_{2},z_{2})= (4, -2, -3)

Therefore,

D =

=

=

=

Distance between points R and S is units.

(iv) C(9, -12, -8) and the origin

Coordinates of origin are (0, 0, 0)

Here, (x_{1},y_{1},z_{1})= (9, -12, -8)

(x_{2},y_{2},z_{2})= (0, 0, 0)

Therefore,

D =

=

=

= = 17

Distance between points C and origin is 17 units.

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