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

Engineering

Mathematics

Line of Greatest Slope

Question

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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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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