Vector Algebra JEE Main Practice Test 2026 | Important Questions

Vector Algebra – JEE Main Practice Test

This Vector Algebra JEE Main Practice Test contains exam-level questions from dot product, cross product, vector equations and applications. Attempt all questions and check your final score.

Q1. Let a = 3i + 2j + k, b = 2i − j + 3k and c be a vector such that (a + b) × c = 2(a × b) + 24j − 6k and (a − b + i) · c = −3. Then |c|² is:
Correct Answer: 38
Q2. The area of the quadrilateral with vertices A(2,1,1), B(1,2,5), C(−2,−3,5), D(1,−6,−7) is:
48
8√38
54
9√38
Q3. Let a = i − 3j + 7k, b = 2i − j + k and c be a vector such that (a + 2b) × c = 3(c × a). If a · c = 130, then b · c is:
Correct Answer: 30
Q4. Let |b| = 1 and |b × a| = 2. Then |(b × a) − b|² is:
1
3
5
4
Q5. For λ > 0, vectors a = i + λj − 3k and b = 3i − j + 2k are such that (a + b) ⟂ (a − b). Then (14 cosθ)² is:
25
50
20
40
Q6. Let a = 2i − j + 3k, b = 3i − 5j + k and c be a vector such that a × c = a × b = c × b and (a + c) · (b + c) = 168. Maximum value of |c|² is:
77
154
308
462
Q7. Let a = i + j + k, b = 2i + 2j + k and d = a × b. If c is a vector such that a · c = |c|, |c − 2a|² = 8 and angle between d and c is π/4, then |10 − 3b · c| + |d × c|² is:
Correct Answer: 6
Q8. Let a = 3i + j − k and c = 2i − 3j + 3k. If b is such that a = b × c and |b|² = 50, then |72 − |b + c|²| is:
Correct Answer: 66
Q9. Vector a = −i + 2j + k is rotated through a right angle passing through y-axis and resulting vector is b. Projection of 3a + √2 b on c = 5i + 4j + 3k is:
√6
2√3
1
3√2
Q10. Let a = i + 2j + k, b = 3i − 3j + 3k and c = 2i − j − k. If b × d = c × d and a · d = 4, then |a × d|² is:
Correct Answer: 128
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