Vector Algebra - JEE Advanced PYQ | Last 5 years | PYQ Khazana #jeeadvancedPYQ

Let OP= α-1/α i+j+k, OQ= î+β-1/βj+k and OR=î+j+2k be three vectors, where α,βR -{O} and O denotes the origin. If (OP×OQ). OR = 0 and the point (a, ß,2) lies on the plane 3x+3y -z +l = 0, then the value of l is____. Let p =2i + j +3k and q = i - j + k. If for some real numbers α, ß, and y, we have 15î+10j+6k=α(2p+q)+ß(p-2q)+y(pxq), then the value of y is____. Let the position vectors of the points P,Q,R and S be a= 1+2j-5k, b=31+6j+3k, c=7i+16j+7k and d= 2î + j+k, respectively. Then which of the following statements is true? (A) The points P,Q,R and S are NOT coplanar (B) b+2d/3 is the position vector of a point which divides PR internally in the ratio 5 : 4 (C) b+2d/3 is the position vector of a point which divides PR externally in the ratio 5 : 4 (D) The square of the magnitude of the vector bxd is 95 Let î, j and k be the unit vectors along the three positive coordinate axes. ã=3î+j-k, b=i+b2j+b3k, č=c1+c2j+c3k, be three vectors such that b2b3 greater than 0, a . b = 0 Let u, v and w be vectors in three-dimensional space, where u and v are unit vectors which are not perpendicular to each other and u.w=1, v.w=1, w.w =4 If the volume of the parallelopiped, whose adjacent sides are represented by the vectors u, v and w, is v2 , then the value of 3u+5v is __ Let O be the origin and OA =2i+2j+k, OB= i-2j+2k and OC =1/2(OB-OA) for some a 0. If |OBxOC|=9/2, then which of the following statements is (are) TRUE? Let a and b be positive real numbers. Suppose PQ=ai+bj and PS=ai-bj are adjacent sides of a parallelogram PQRS. Let u and v be the projection vectors of w = i + j along PQ and PS, respectively. If u +v = w and if the area of the parallelogram PQRS is 8, then which of the following statements is/are TRUE ? (A) Projection of OCon OA is -3/2 (B) Area of the triangle OAB is 9/2 (C) Area of the triangle ABC is 9/2 (D) The acute angle between the diagonals of the parallelogram with adjacent sides OA and OC is π/3 Download JEE Main & Advanced PYQs https://1learn.in/new-courses/43/cont... Enrol in InfinIITy 2.0 Dropper Batch: https://1learn.in/new-courses/71-infi... ProdJEE batch (Class 12): https://1learn.in/quick-pay/10/65 EnerJEE batch (Class 11) https://1learn.in/quick-pay/10/64 👉Whatsapp: https://whatsapp.com/channel/0029Va9s... 👉Telegram: https://t.me/jeeudaan ✅Download JEE One App for Unlimited Free study material & TESTS in NTA pattern) : https://bit.ly/3vc809M #jee1 #jeeone #jeeadvanced #jeemains #iitjee #exampreparation #competitiveexams #problemsolving #examtips #jeemain2026 #jeeadvanced2026 #jeeadvanced2027 #jeemain2026news #jeemain2027news #jeemain2027 #previousyearquestions #tipsandtricks #testtakingstrategies #jeepreparation #jeemainnews #jeeadvancedpreparation #jeeadvancedsolutions #jeeexamtips #jeepractice #pyq #teamudaan #jeeadvancedpyq #vectoralgebra #jeemathquestions #mathpyq jee 1,namo kaul,nta news,jee main 2026 news,jee main news,jee main 206 latest update,jee main 2026 update,jee main 2026 latest news,nta latest news,jee advanced 2026,jee advanced 2026 strategy,strategy for jee advanced 2026,strategy for jee advanced,jee advanced preparation strategy 2026,jee advanced 2026 preparation,jee 2026 roadmap,strategy for jee 2026,jee 2026 preparation strategy,jee advanced strategy,jee advanced block strategy,jee advanced 2026 mcq,jee advanced 2027,jee main 2027 strategy,jee main 2027 preparation,jee 2027 roadmap,strategy for jee 2027,jee 2027 preparation strategy,important jee main 2027 pyq,jee main 2027 previous year questions,jee main 2027 mcq,jee advanced toughest questions,jee adavnced toughest problems,jee advanced problem solving,important jee advanced 2026 pyq,jee advanced math pyq,math important pyq,previous year question paper for jee advanced,jee advanced previous year math questions,math important pyqs,jee advanced 2026 previous year questions,important jee advanced pyqs,important jee advanced topics,math important topics