Mathematics · JEE

Online Practice: Scalar and vector products for JEE

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Sharpen your mathematics preparation with interactive online practice for Scalar and vector products. Goodmarks offers 17+ JEE-style MCQs mapped to the official syllabus, each with detailed explanations so you learn from every attempt.

Syllabus context

Part of Vector Algebra in JEE Main Mathematics.

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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

If position vectors of four vertices of a square are

\boldsymbol{A}=\mathbf{3} \boldsymbol{i}-\boldsymbol{\lambda} \boldsymbol{j}, \boldsymbol{B}=\mathbf{9} \boldsymbol{i}-\boldsymbol{6} \boldsymbol{k}

\boldsymbol{C}=\mathbf{6} \boldsymbol{j}-\mathbf{5} \boldsymbol{k}

and

\boldsymbol{D}=\boldsymbol{\alpha} \boldsymbol{i}-\boldsymbol{3} \boldsymbol{j}+\boldsymbol{4} \boldsymbol{k}

then value of

\lambda-\alpha

is :

Q5MathsUnit 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.

Q6MathsUnit 12: Vector Algebra

\boldsymbol{A}=(\mathbf{1}, \mathbf{2}, \mathbf{3}), \boldsymbol{B}=(\mathbf{2}, \mathbf{3}, \mathbf{4})

and

\boldsymbol{A} \boldsymbol{B}

is produced upto

C

such that

2 A B=B C

then

C=

Q7MathsUnit 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

Q8MathsUnit 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)

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Frequently asked questions

How do I practice Scalar and vector products online for JEE?

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How many Scalar and vector products questions are available?

Goodmarks currently has 17+ JEE-aligned MCQs for Scalar and vector products, with more added regularly.

Is this aligned with the JEE Main syllabus?

Yes. All Mathematics questions on Goodmarks are organised by official JEE Main units and subtopics, including Scalar and vector products.

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Every question includes the correct answer and a step-by-step explanation. Free users can practise a random mix; Pro unlocks full subject and topic filters.