Mathematics · JEE

Scalar and vector products Previous Year Questions for JEE

7+ syllabus-aligned questions available

Quick answer

Goodmarks offers 7+ JEE-style PYQs for Scalar and vector products with detailed solutions. While official past papers rotate yearly, our bank covers the same concepts, difficulty, and question formats tested in JEE Mathematics.

Previous year questions are the fastest way to understand how Scalar and vector products is tested in JEE. Practise 7+ exam-pattern MCQs modelled on JEE Main and Advanced, with full solutions for every question.

Free sample questions

Attempt 7 free MCQs for Scalar and vector products. Unlock the full bank with Pro.

Unlock full bank

Q1MathsUnit 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

Q2MathsUnit 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)

Q3MathsUnit 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 :

Q4MathsUnit 12: Vector Algebra

In a triangle

A B C,

right angled at the vertex

A,

if the position vectors

A, B

and

C

are respectively

3 \tilde{i}+\tilde{j}-\tilde{k},-\tilde{i}+

\mathbf{3} \tilde{j}+p \tilde{k}

and

5 \tilde{i}+q \tilde{j}-4 \tilde{k},

then the point

(p, q)

lies on a line

Q5MathsUnit 12: Vector Algebra

Given

\left|\overrightarrow{\boldsymbol{A}}_{1}\right|=2,\left|\overrightarrow{\boldsymbol{A}}_{2}\right|=\overrightarrow{\mathbf{3}}

and

\left|\vec{A}_{1}+\vec{A}_{2}\right|=3 .

Find the value of

\left(\overrightarrow{\boldsymbol{A}}_{1}+\mathbf{2} \overrightarrow{\boldsymbol{A}}_{2}\right) \cdot\left(\boldsymbol{3} \overrightarrow{\boldsymbol{A}}_{1}-\boldsymbol{4} \boldsymbol{\vec { A }}_{2}\right)

Q6MathsUnit 12: Vector Algebra

Assertion Let

\bar{a}, \bar{b}, \bar{r}

be the vectors such that

\bar{r}+

\overline{\boldsymbol{r}} \times \overline{\boldsymbol{a}}=\overline{\boldsymbol{b}} \operatorname{then}|\overline{\boldsymbol{r}}|^{2}=\frac{(\overline{\boldsymbol{a}} \cdot \overline{\boldsymbol{b}})^{2}+|\overline{\boldsymbol{b}}|^{2}}{\mathbf{1}+|\overline{\boldsymbol{a}}|^{2}}

Reason

\overline{\boldsymbol{r}}=\frac{(\overline{\boldsymbol{a}} \cdot \overline{\boldsymbol{b}}) \overline{\boldsymbol{a}}+\overline{\boldsymbol{b}}+\overline{\boldsymbol{a}} \times \overline{\boldsymbol{b}}}{\mathbf{1}+|\overline{\boldsymbol{a}}|^{2}}

Q7MathsUnit 12: Vector Algebra

Equation of the plane containing the

\operatorname{lines} \overline{\boldsymbol{r}}=(\overline{\boldsymbol{i}}-\boldsymbol{2} \overline{\boldsymbol{j}}+\overline{\boldsymbol{k}})+\boldsymbol{t}(\overline{\boldsymbol{i}}+\mathbf{2} \overline{\boldsymbol{j}}-\overline{\boldsymbol{k}})

\boldsymbol{\boldsymbol { r }}=(\overline{\boldsymbol{i}}+\mathbf{2} \overline{\boldsymbol{j}}-\overline{\boldsymbol{k}})+\boldsymbol{s}(\overline{\boldsymbol{i}}+\overline{\boldsymbol{j}}+\mathbf{3} \overline{\boldsymbol{k}})

Want unlimited Scalar and vector products practice?

Pro unlocks the full question bank, topic filters, and attempt history.

Get started free View Pro plans

Frequently asked questions

Why practise PYQs for Scalar and vector products?

PYQs reveal recurring concepts, common traps, and the difficulty level JEE expects. Solving them builds exam temperament and time management.

Does Goodmarks have actual JEE past papers?

Our bank includes exam-style MCQs aligned with JEE Main Mathematics syllabus for Scalar and vector products, covering the same topics as previous year papers.

How should I use PYQs for Vector Algebra?

Solve timed sets, review every explanation, note weak subtopics, then revisit with focused practice on Goodmarks.

Are PYQ solutions step-by-step?

Yes. Every question includes the correct answer and a detailed explanation showing the reasoning.