Find the point on Z-axis which are at a distance unit from the point (1,2,3).

Engineering

Mathematics

Direction Cosines and Direction Ratio

Equation of Straight Line in 3D

Distance Formulae and Its Application

Question

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

College PredictorLive

Know your College Admission Chances Based on your Rank/Percentile, Category and Home State.

Get your JEE Main Personalised Report with Top Predicted Colleges in JoSA

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

z² – 6z – 7 = 0

z = 7, z = –1

Hence points are (0,0,7), (0,0,–1).