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Scalar and Vector Products for JEE: 17 solved questions

Real JEE paper questions on scalar and vector products, part of motion in a plane. Each opens with the options, the correct answer and a step-by-step solution. Papers run from 2004 to 2025. No sign-in needed to read them.

What this topic asks

• Vector product — 9 questions
• Scalar product and projections — 8 questions

All 17 questions with solutions

• If two vectors ⃗P = ̂i + 2m̂j + m̂k and ⃗Q = 4̂i - 2̂j + m̂k are perpendicular to each other. Then, the value… JEE Main 24th Jan 2nd Shift 2023
• ⃗A is a vector quantity such that |⃗A| = non-zero constant. Which of the following expression is true for ⃗A? JEE Main 25th June 1st Shift 2022
• If ⃗A and ⃗B are two vectors satisfying the relation ⃗A·⃗B = |⃗A×⃗B|. Then the value of |⃗A - ⃗B| will be JEE Main 20th July 1st Shift 2021
• What will be the projection of vector ⃗A = ̂i + ̂j + ̂k on vector ⃗B = ̂i + ̂j? JEE Main 22nd July 2nd Shift 2021
• The incident ray, reflected ray and the outward drawn normal are denoted by the unit vectors ⃗a, ⃗b and ⃗c re… JEE Main 26th Feb 2nd Shift 2021
• Let |⃗A₁| = 3, |⃗A₂| = 5 and |⃗A₁ + ⃗A₂| = 5. The value of (2⃗A₁ + 3⃗A₂)·(3⃗A₁ - 2⃗A₂) is JEE Main 8th April 2nd Shift 2019
• Let ⃗A = (̂i + ̂j) and ⃗B = (2̂i - ̂j). The magnitude of a co-planar vector ⃗C such that ⃗A·⃗C = ⃗B·⃗C = ⃗A·⃗… JEE Main Online 2018
• If ⃗A×⃗B = ⃗B×⃗A, then the angle between ⃗A and ⃗B is AIEEE 2004
• Two particles are located at equal distance from origin. The position vectors of those are represented by ⃗A… JEE Main 23rd Jan 2nd Shift 2025
• For three vectors ⃗A = (-x̂i - 6̂j - 2̂k), ⃗B = (-̂i + 4̂j + 3̂k) and ⃗C = (-8̂i - ̂j + 3̂k), if ⃗A·(⃗B×⃗C) =… JEE Main 6th April 1st Shift 2024
• Vectors âi + b̂j + ̂k and 2̂i - 3̂j + 4̂k are perpendicular to each other when 3a + 2b = 7, the ratio of a t… JEE Main 24th Jan 1st Shift 2023
• If ⃗P = 3̂i + √3̂j + 2̂k and ⃗Q = 4̂i + √3̂j + 2.5̂k then, the unit vector in the direction of ⃗P×⃗Q is 1/x(√… JEE Main 25th Jan 1st Shift 2023
• If ⃗A = (2̂i + 3̂j - ̂k) m and ⃗B = (̂i + 2̂j + 2̂k) m. The magnitude of component of vector ⃗A along vector… JEE Main 26th July 2nd Shift 2022
• Three particles P, Q and R are moving along the vectors ⃗A = ̂i + ̂j, ⃗B = ̂j + ̂k and ⃗C = -̂i + ̂j respecti… JEE Main 22nd July 2nd Shift 2021
• If ⃗P×⃗Q = ⃗Q×⃗P, the angle between ⃗P and ⃗Q is θ (0° < θ < 360°). The value of θ will be °. JEE Main 25th Feb 2nd Shift 2021
• In the cube of side a shown in the figure, the vector from the central point of the face ABOD to the central… JEE Main 10th Jan 1st Shift 2019
• If the projection of 2̂i + 4̂j - 2̂k on ̂i + 2̂j + α̂k is zero. Then, the value of α will be . JEE Main 28th July 1st Shift 2022