Question
Download Solution PDFIf the projections of a straight line segment on the coordinate axes are 6, 8, 0, then the length of the segment is
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
The direction cosines of the vector is the corresponding coordinate of the vector divided by the length of the vector.
If l, m, and n are direction cosines,then l2 + m2 + n2 = 1
Calculation:
The projections of a straight line segment on the coordinate axes are 6, 8, 0
Let, l, m, and n be the direction cosines of a given line and k is the length of a straight line
So, l = 6/k ⇒ lk = 6
m = 8/k ⇒ mk = 8
n = 0/k ⇒ nk = 0
Now,
\(\rm (lk)^2+(mk)^2+(nk)^2 =6^2+8^2 +0^2 \\ \Rightarrow (l^2+m^2+n^2)k^2=36+64+0 \\\Rightarrow (1)k^2=100\;\;\;\;\;(\because l^2+m^2+n^2=1) \\\Rightarrow k = 10\)
Hence, option (1) is correct.
Last updated on Jul 11, 2025
->Indian Airforce Agniveer (02/2026) Online Form Link has been activated at the official portal. Interested candidates can apply between 11th July to 31st July 2025.
->The Examination will be held 25th September 2025 onwards.
-> Earlier, Indian Airforce Agniveer Group X 2025 Last date had been extended.
-> Candidates applied online from 7th to 2nd February 2025.
-> The online examination was conducted from 22nd March 2025 onwards.
-> The selection of the candidates will depend on three stages which are Phase 1 (Online Written Test), Phase 2 ( DV, Physical Fitness Test, Adaptability Test), and Phase 3 (Medical Examination).
-> The candidates who will qualify all the stages of selection process will be selected for the Air Force Group X posts & will receive a salary ranging of Rs. 30,000.
-> This is one of the most sought jobs. Candidates can also check the Airforce Group X Eligibility here.