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Friday, 9 October

JEE Main 2025 · MathsMultiple choiceSingle correctMediumApplication

JEE Main 8 April 2025, Shift 2, Maths Q14

Question 14 of 75 in this shift, Maths question 14 of 25, Section A.

Let 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 the vectors a⃗\vec{a} and b⃗\vec{b} and be perpendicular to a⃗\vec{a}. Then such a vector c^\hat{c} is :
  1. (1)13(i^−j^+k^)\frac{1}{\sqrt{3}}(\hat{i} - \hat{j} + \hat{k})
  2. (2)13(−i^+j^−k^)\frac{1}{\sqrt{3}}(-\hat{i} + \hat{j} - \hat{k})
  3. (3)12(−i^+k^)\frac{1}{\sqrt{2}}(-\hat{i} + \hat{k})Official answer
  4. (4)15(j^−2k^)\frac{1}{\sqrt{5}}(\hat{j} - 2\hat{k})

Official answer

Option 3

NTA final key.

Chapter
Vector Algebra
Topic
Dot Product
Idea tested
Orthogonal Resolution of a Vector

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 2024, Shift 1 · Q18The set of all α\alpha, for which the vectors a⃗=αti^+6j^−3k^\vec{a}=\alpha t\hat{i}+6\hat{j}-3\hat{k} and…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 42 of the 174 JEE Main shifts held from 2017 to 2026.