Question
Download Solution PDFIf the origin and the points P(2, 3, 4), Q(1, 2, 3) and R(x, y, z) are co-planar then
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
If the three vectors are coplanar then their scalar triple product is zero..
⇒\(\rm \vec a.(\vec b\times \vec c) = 0\)
Calculations:
Given the origin (0, 0, 0) and the points P(2, 3, 4), Q(1, 2, 3) and R(x, y, z) are co-planer
⇒ \(\rm \vec a = \vec {OR} = {(x, y, z)}\)
⇒ \(\rm \vec b = \vec {OP} = {(2, 3, 4)}\)
⇒ \(\rm \vec c = \vec {OQ} = {(1, 2, 3)}\)
Here, \(\rm\vec a\), \(\rm\vec b\) and \(\vec c\)are co planer
The three vectors are coplanar if their scalar triple product is zero..
⇒\(\rm \vec a.(\vec b\times \vec c) = 0\)
⇒\(\begin{vmatrix} \rm x & \rm y & \rm z\\ 2&3 &4 \\ 1&2 &3 \end{vmatrix} = 0\)
⇒ x(9 - 8) - y(6 - 4) + z (4 - 3) = 0
⇒ x - 2y + z = 0
Hence, if the origin and the points P(2, 3, 4), Q(1, 2, 3) and R(x, y, z) are co-planar then x - 2y + z = 0
Last updated on Jun 30, 2025
->Indian Airforce Agniveer (02/2026) Notification has been released. 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.