Find the point on Z-axis which are at a distance \sqrt{21} unit from the point\left(\right. 1 , 2 , 3 \left.\right)

Engineering

Mathematics

Line of Greatest Slope

Question

Find the point on Z-axis which are at a distance

\sqrt{21}

unit from the point

(1, 2, 3)

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Let the point on Z axis be given as

(0, 0, z)

. The distance between

(1, 2, 3)

and

(0, 0, z)

is given as

\sqrt{1^{2} + 2^{2} + (3 - z)^{2}} = \sqrt{21}

5 + (3 - z)^{2} = 21

z^{2} - 6 z - 7 = 0

z = 7, z = - 1

Hence points are

(0, 0, 7), (0, 0, - 1)

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