JEE 2023 Mathematics PYQ — Let be the origin and the position vector of the point be . If th… | Mathem Solvex | Mathem Solvex
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JEE 2023 — Mathematics PYQ
JEE | Mathematics | 2023
Let O be the origin and the position vector of the point P be −i^−2j^+3k^. If the position vectors of the A,B and C are 2i^+j^−3k^, −2i^+4j^−2k^ and −4i^+2j^−k^ respectively, then the projection of the vector OP on a vector perpendicular to the vectors AB and AC is:
Choose the correct answer:
A.
511
(Correct Answer)
B.
38
C.
37
D.
3
Correct Answer:
511
Explanation
1. Identify the given vectors
OP=−i^−2j^+3k^
OA=2i^+j^−3k^
OB=−2i^+4j^−2k^
OC=−4i^+2j^−k^
2. Calculate AB and AC
AB=OB−OA=(−2−2)i^+(4−1)j^+(−2+3)k^=−4i^+3j^+k^
AC=OC−OA=(−4−2)i^+(2−1)j^+(−1+3)k^=−6i^+j^+2k^
3. Find the perpendicular vector (n)
The vector perpendicular to both AB and AC is given by their cross product n=AB×AC:
n=i^−4−6amp;j^amp;3amp;1amp;k^amp;1amp;2
n=i^(6−1)−j^(−8+6)+k^(−4+18)
n=5i^+2j^+14k^
4. Calculate the projection
The projection of vector a on vector b is ∣b∣∣a⋅b∣.
