Question
Download Solution PDFThe sum of distances from origin to (0, 5, 5) and (5, 8, 6) is:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Two points are (0, 5, 5) and (5, 8, 6).
Concept:
Distance between two points \(\rm (x_1,y_2,z_3) and(x_2,y_2,z_3)\) is
\(\rm \sqrt{(x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2}\)
Calculation:
Distance form origin (0,0,0) to point (0,5,5) is
\(\rm d_1=\sqrt{(0)^2+(5)^2+(5)^2}\)
\(\rm d_1=5\sqrt{2}\)
Distance form origin (0,0,0) to point (5,8,6) is
\(\rm d_2=\sqrt{(5)^2+(8)^2+(6)^2}\)
\(\rm d_2=5\sqrt5\)
Now the sum of distances from origin to (0, 5, 5) and (5, 8, 6) is
\(\rm d=d_1+d_2\)
\(\rm d=5\sqrt{2}+5\sqrt{5}\)
\(\rm d=5(\sqrt{2}+\sqrt{5})\)
Hence the option (4) is correct.
Last updated on May 26, 2025
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