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Saturday, 31 October

JEE Main 2022 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 25 June 2022, Shift 1, Maths Q14

Question 14 of 90 in this shift, Maths question 14 of 30, Section A.

Let a⃗=a1i^+a2j^+a3k^\vec{a}=a_1\hat{i}+a_2\hat{j}+a_3\hat{k} ai>0a_i>0, i=1,2,3i=1,2,3 be a vector which makes equal angles with the coordinate axes OX, OY and OZ. Also, let the projection of a⃗\vec{a} on the vector 3i^+4j^3\hat{i}+4\hat{j} be 7. Let b⃗\vec{b} be a vector obtained by rotating a⃗\vec{a} with 90∘90^\circ. If a⃗\vec{a}, b⃗\vec{b} and xx-axis are coplanar, then projection of a vector b⃗\vec{b} on 3i^+4j^3\hat{i}+4\hat{j} is equal to :
  1. (1)7\sqrt{7}
  2. (2)2\sqrt{2}Official answer
  3. (3)22
  4. (4)77

Official answer

Option 2

NTA final key.

Chapter
Vector Algebra
Topic
Dot Product
Idea tested
Vectors with Equal Inclination

Same topic in other shifts

All Dot Product questions
  1. 2 Apr 2026, Shift 1 · Q14If a⃗\vec a and b⃗\vec b are two vectors such that ∣a⃗∣=2|\vec a|=2 and ∣b⃗∣=3|\vec b|=3, then the maximum value of…HardSingle correct
  2. 2 Apr 2026, Shift 2 · Q14Let the vectors a⃗=−i^+j^+3k^\vec{a} = -\hat{i} + \hat{j} + 3\hat{k} and b⃗=i^+3j^+k^\vec{b} = \hat{i} + 3\hat{j} + \hat{k}. For some…MediumSingle correct
  3. 2 Apr 2026, Shift 2 · Q16Two adjacent sides of a parallelogram PQRSPQRS are given by PQ⃗=j^+k^\vec{PQ} = \hat{j} + \hat{k} and PS⃗=i^−j^\vec{PS} = \hat{i} - \hat{j}. If the side…MediumSingle correct
  4. 2 Apr 2025, Shift 1 · Q11If a⃗\vec{a} is a nonzero vector such that its projections on the vectors 2i^−j^+2k^2\hat{i}-\hat{j}+2\hat{k}, i^+2j^−2k^\hat{i}+2\hat{j}-2\hat{k} and…MediumSingle correct
  5. 7 Apr 2025, Shift 2 · Q15Let a⃗\vec{a} and b⃗\vec{b} be the vectors of the same magnitude such that…MediumSingle correct
  6. 8 Apr 2025, Shift 2 · Q14Let a⃗=i^+2j^+k^\vec{a} = \hat{i} + 2\hat{j} + \hat{k} and b⃗=2i^+j^−k^\vec{b} = 2\hat{i} + \hat{j} - \hat{k}. Let c^\hat{c} be a unit vector in the plane of…MediumSingle correct

Question text from the official JEE Main paper published by NTA; answer from the final answer key. Chapter, topic and idea tags, difficulty and skill are Lumi’s. Lumi analyses 108 of the 174 JEE Main shifts held from 2017 to 2026.