Vector JEE Questions PDF with Solution, Practice Now

Vector JEE Questions: Vectors are an important topic in Mathematics, and they are a very big part of JEE Main and JEE Advanced exams. This topic comes under Vector Algebra, which is useful in both pure math and physics. Vectors help us understand direction and magnitude, so they are not only in maths but also in physics chapters like motion, force, and 3D geometry.

The topic has a good weightage in JEE exams, as every year 10–12 questions are asked in JEE Main and sometimes even more in JEE Advanced. If you know this topic well, you can easily score marks because vector algebra questions are very straightforward once you understand the formulas.

Practicing vector questions JEE Mains and JEE Advanced vector problems will make your concepts clear, and it will also improve your problem-solving speed. Students who practice important vector algebra questions JEE regularly get more confidence in handling tricky problems in the exam.

Check: JEE Main Syllabus

Vector JEE Questions Overview

The importance of vectors in JEE exams cannot be ignored. This topic is connected with other areas of mathematics like 3D geometry and coordinate geometry, and also with physics mechanics. Because of this, questions from this chapter become natural and direct. The JEE exam pattern covers multiple-choice questions, numerical value type questions, and integer type questions, and vector algebra questions JEE can appear in all these formats. Students who practice well can easily score marks here because the calculations are straightforward if the formulas are remembered properly.

Practice Vector JEE Questions

Here are some practice questions that follow the JEE exam pattern. These include MCQs and numerical value types.

Single Correct Type Questions

1. â, b̂ and â – b̂ are unit vectors. The volume of the parallelepiped, formed with â, b̂ and â × b̂ as coterminous edges is:

A. 1
B. 1/4
C. 2/3
D. 3/4

2. A line passing through P(3, 7, 1) and R(2, 5, 7) meets the plane 3x + 2y + 11z – 9 = 0 at Q. Then PQ is equal to:

A. 5√41/59
B. √41/59
C. 50√41/59
D. 25√41/59

3. If a̅, b̅ and c̅ are three non-zero non-coplanar vectors and p̅ = a̅ + b̅ – 2c̅; q̅ = 3a̅ – 2b̅ + c̅ and r̅ = a̅ – 4b̅ + 2c̅ are three vectors such that the volumes of the parallelepiped formed by a̅, b̅, c̅ and p̅, q̅, r̅ as their coterminous edges are V₁ and V₂ respectively. Then V₂/V₁ is equal to:

A. 10
B. 15
C. 20
D. None of these

4. If the two lines represented by x + ay = b; z + cy = d and x = ay + b; z = cy + d be perpendicular to each other, then the value of aa + cc is:

A. 1
B. 2
C. 3
D. 4

5. The distance between the line r̅ = 2ĵ – 2î + 3k̂ + λ(î + 5ĵ + k̂) and the plane r̅·(î + 5ĵ + k̂) = 5 is:

A. 10/9
B. 10/3√3
C. 3/10
D. 10/3

6. If (a̅ × b̅) × c̅ = a̅ × (b̅ × c̅), where a̅, b̅ and c̅ are any three vectors such that a̅·b̅ ≠ 0, b̅·c̅ ≠ 0 then a̅ and c̅ are:

A. Inclined at an angle of π/3
B. Inclined at an angle of π/6
C. Perpendicular
D. Parallel

7. Let r̅ be position vector of variable point in cartesian plane OXY such that r̅·(r̅ + 6ĵ) = 7 cuts the co-ordinate axes at four distinct points, then the area of the quadrilateral formed by joining these points is:

A. 4√7
B. 6√7
C. 7√7
D. 8√7

8. If |a̅| = 2, |b̅| = 5 and a̅·b̅ = 0 then a̅ × (a̅ × (a̅ × (a̅ × (a̅ × b̅))))) is equal to

A. 64îa̅
B. 64b̅
C. –64îa̅
D. –64b̅

9. If O (origin) is a point inside the triangle PQR such that OṔ + k₁OQ̅ + k₂OR̅ = 0 where k₁, k₂ are constants such that Area(ΔPQR) / Area(ΔOQR) = 4, then the value of k₁ + k₂ is:

A. 2
B. 3
C. 4
D. 5

Vector JEE Questions PDF with Solution

For better practice, PW provides a Vector JEE Questions PDF with answer and solution. This PDF contains solved vector questions JEE Mains, JEE Advanced vector problems, and important vector algebra questions JEE. Students can download and revise anytime before exams.