JEE 2023 — Mathematics PYQ
JEE | Mathematics | 2023The distance of the point (−1,9,−16) from the plane 2x+3y−z=5 measured parallel to the line 3x+4=42−y=12z−3 is:
Choose the correct answer:
- A.
31
- B.
132
- C.
202
26
Explanation
-
Line ki equation (standard form): Dhyan rahe ki 2−y ko hum −(y−2) likhte hain, toh direction ratios (3,−4,12) honge.
3x+4=−4y−2=12z−3=λ -
Point P(−1,9,−16) se guzarne wali line jo di gayi line ke parallel ho:
3x+1=−4y−9=12z+16=r -
General point on this line:
x=3r−1,y=−4r+9,z=12r−16 -
Plane ki equation jisme ye point satisfy hona chahiye:
2x+3y−z=5
Isme x,y,z ki value rakh kar aap r nikal sakte hain, aur phir distance formula d=(x2−x1)2+(y2−y1)2+(z2−z1)2 se answer mil jayega. Is sawal ka sahi jawab (D) 26 hai.
Explanation
-
Line ki equation (standard form): Dhyan rahe ki 2−y ko hum −(y−2) likhte hain, toh direction ratios (3,−4,12) honge.
3x+4=−4y−2=12z−3=λ -
Point P(−1,9,−16) se guzarne wali line jo di gayi line ke parallel ho:
3x+1=−4y−9=12z+16=r -
General point on this line:
x=3r−1,y=−4r+9,z=12r−16 -
Plane ki equation jisme ye point satisfy hona chahiye:
2x+3y−z=5
Isme x,y,z ki value rakh kar aap r nikal sakte hain, aur phir distance formula d=(x2−x1)2+(y2−y1)2+(z2−z1)2 se answer mil jayega. Is sawal ka sahi jawab (D) 26 hai.