Mathematics · JEE

Scalar and vector products Concepts for JEE

14+ syllabus-aligned questions available

Quick answer

Master Scalar and vector products by understanding definitions, standard results, and typical JEE question patterns — then practise with syllabus-aligned MCQs on Goodmarks.

Build clear conceptual foundations for Scalar and vector products before speed practice. This guide covers what JEE expects and how to test yourself with MCQs.

Concept explainer

Scalar and vector products is a core JEE Main Mathematics subtopic under Vector Algebra. Master the definitions, standard results, and typical MCQ patterns tested in JEE Main and Advanced.

Key points

Understand the definition and scope of Scalar and vector products in the JEE syllabus
Memorise key formulas and standard results linked to Scalar and vector products
Practise 20–40 syllabus-aligned MCQs with step-by-step solutions

JEE tips

Revise Scalar and vector products with a one-page formula sheet before attempting mixed tests
After each practice set, log mistakes specific to Scalar and vector products and reattempt after 48 hours

Common trap

Students often rush Scalar and vector products questions without checking units, sign conventions, or boundary conditions — always verify assumptions before calculating.

Syllabus context

Part of Vector Algebra in JEE Main Mathematics.

Free sample questions

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Q1MathsUnit 12: Vector Algebra

Let

a, \beta, \gamma

be distinct real numbers. The points with position vectors ai

+\beta j+

\gamma k, \beta i+\gamma j+a k, \gamma i+a j+\beta k

Q2MathsUnit 12: Vector Algebra

The non zero vector

\vec{a}, \vec{b}, \vec{c}

related by

\vec{a}=8 \vec{b}

and

\vec{c}=-7 \vec{b},

then angle between

\vec{a} \& \vec{c}

Q3MathsUnit 12: Vector Algebra

Consider

\Delta A B C

with

A \equiv(\vec{a}), B \equiv(\vec{b})

and

C=(\vec{c}),

\vec{b} .(\vec{a}+\vec{c})=\vec{b} \cdot \vec{b}+

\vec{a} \cdot \vec{c} ;|\vec{b}-\vec{a}|=3 ;|\vec{c}-\vec{b}|=4

then the angle between the medians

\overline{A M}

and

B D

Q4MathsUnit 12: Vector Algebra

For any four points

P, Q, R, S

|\overrightarrow{P Q} \times \overrightarrow{\boldsymbol{R}} \boldsymbol{S}-\overrightarrow{\boldsymbol{Q} \boldsymbol{R}} \times \overrightarrow{\boldsymbol{P}} \boldsymbol{S}+\overrightarrow{\boldsymbol{R}} \boldsymbol{P} \times \overrightarrow{\boldsymbol{Q}} \boldsymbol{S}|

is equal to 4 times the area of the triangle.

Q5MathsUnit 12: Vector Algebra

a, b, c

are non-coplanar vectors and

\lambda

is a real number, then

\left[\lambda(\vec{a}+\vec{b}) \lambda^{2} \vec{b} \lambda \vec{c}\right]=[\vec{a} \quad \vec{b}+\vec{c} \quad \vec{b}]

for

Q6MathsUnit 12: Vector Algebra

The points

A(-1,3,0), B(2,2,1)

and

C(1,1,3)

determine a plane. The distance of the plane

A, B, C

from the point

D(5,7,8)

Q7MathsUnit 12: Vector Algebra

The vectors

\hat{\boldsymbol{i}}+\boldsymbol{2} \hat{\boldsymbol{j}}+\boldsymbol{3} \hat{\boldsymbol{k}}, \boldsymbol{2} \hat{\boldsymbol{i}}-\hat{\boldsymbol{j}}+\hat{\boldsymbol{k}}

and

\mathbf{3} \hat{\mathbf{i}}+\hat{\boldsymbol{j}}+\mathbf{4} \hat{\boldsymbol{k}}

are so placed that the end point of one vector is the starting point of the next vector. Then the vectors are :

Q8MathsUnit 12: Vector Algebra

\vec{V}=3 \hat{i}+4 \hat{j}

then, with what scalar 'C must it be multiplied so that

C|\overrightarrow{\boldsymbol{V}}|=

\mathbf{7 . 5}:

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Frequently asked questions

What concepts in Scalar and vector products are essential for JEE?

Focus on core ideas across Scalar and vector products. JEE tests application, not just memorisation.