JEE 2023 — Mathematics PYQ
JEE | Mathematics | 2023Let the foot of the perpendicular of the point P(3,−2,−9) on the plane passing through the points (−1,−2,−3),(9,3,4),(9,−2,1) be Q(α,β,γ). Then, the distance of Q from the origin is:
Choose the correct answer:
- A.
29
- B.
38
42
Explanation
Solution:
Maana points A(−1,−2,−3), B(9,3,4), aur C(9,−2,1) hain.
Plane ka normal vector n=AB×AC hoga:
Simplify karne par direction ratios (2,3,−5) hain.
Plane ki equation (A point se):
Foot of perpendicular Q(α,β,γ) ka formula:
Yahan se values aati hain:
α=3−2=1, β=−2−3=−5, γ=−9+5=−4.
Point Q is (1,−5,−4).
Distance from origin (0,0,0):
Sahi Option: (3)
Explanation
Solution:
Maana points A(−1,−2,−3), B(9,3,4), aur C(9,−2,1) hain.
Plane ka normal vector n=AB×AC hoga:
Simplify karne par direction ratios (2,3,−5) hain.
Plane ki equation (A point se):
Foot of perpendicular Q(α,β,γ) ka formula:
Yahan se values aati hain:
α=3−2=1, β=−2−3=−5, γ=−9+5=−4.
Point Q is (1,−5,−4).
Distance from origin (0,0,0):
Sahi Option: (3)