The points A and B have co-ordinate $(1, 2, 4)$ and $(- 1, 3, 5)$ respectively. Find $A B$ and its magnitude.

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Solution

$A = (1, 2, 3)$
$B = (- 1, 3, 5)$
$A = i + 2 j + 3 k$
$B = - i + 3 j + 5 k$
$A B = B - A$
$A B = (- i + 3 j + 5 k) - (i + 2 j + 3 k)$
$A B = - 2 i + j + 2 k$
$A B = \sqrt{(- 2)^{2} + (1)^{2} + (2)^{2}} = \sqrt{9} = 3$

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