Find the points on z-axis which are at a distance -21 from the point 1-2-3

Let P (0, 0, z) be at a distance of √(21) from Q (1, 2, 3) So, PQ = √((0 1)^2+(0 2)^2+(z 3)^2) √(21)=√((1)^2+(2)^2+(z 3)^2) 21 5=(z 3)^2 16 = (z 3)^2 z 3=±4 z 7 ...

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Byju's Answer

Standard XII

Mathematics

Distance Formula

Find the poin...

Question

Find the points on z-axis which are at a distance $\sqrt{21}$ from the point (1, 2, 3)

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Solution

Let P (0, 0, z) be at a distance of $\sqrt{21}$ from Q (1, 2, 3)

So,

PQ = $\sqrt{(0 - 1)^{2} + (0 - 2)^{2} + (z - 3)^{2}}$

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

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

$16 = (z - 3)^{2}$

$z - 3 = \pm 4$ z-7 and z = -1

So, the required points are (0, 0, 7) and (0, 0, -1)

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Find the points on z-axis which are at a distance √21 from the point (1, 2, 3)

Let P (0, 0, z) be at a distance of √21 from Q (1, 2, 3) So, PQ = √(0−1)2+(0−2)2+(z−3)2 √21=√(1)2+(2)2+(z−3)2 21−5=(z−3)2 16=(z−3)2 z−3=±4 z-7 and z = -1 So, the required points are (0, 0, 7) and (0, 0, -1)

Find the points on z-axis which are at a distance $\sqrt{21}$ from the point (1, 2, 3)