Question

If p (1,2,3) and Q (-1,0,3) are two points then PQ is equal to

Answer 1

Given :-

• Coordinates of P = (1, 2, 3)

• Coordinates of Q = (-1, 0, 3)

To find :-

• Length of PQ

Solution :-

Let's assume that,

• P = ( 1, 2, 3 ) = ( x1, y1, z1 )

• Q = ( -1, 0, 3 ) = ( x2, y2, z2 )

Now, the distance of PQ in 3-D geometry is given by,

$\sf Length\:of\,PQ = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2}$

$\sf Length\:of\,PQ = \sqrt{(-1-1)^2+(0-2)^2+(3-3)^2}$

$\sf Length\:of\,PQ = \sqrt{(-2)^2+(-2)^2}$

$\sf Length\:of\,PQ = \sqrt{4+4}$

$\sf Length\:of\,PQ = \sqrt{8}$

$\sf Length\:of\,PQ = 2\sqrt{2}$

Hence the length of PQ is 2√2 units.