Mathematics · JEE

Important Questions: Vector Algebra for JEE

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The most important Vector Algebra questions for JEE cover conceptual traps, standard results, and numerical patterns from Vectors and scalars, the addition of vectors, Components of a vector in two dimensions and three-dimensional spaces, Scalar and vector products. Goodmarks provides 28+ high-yield MCQs with full solutions.

Focus on what matters most. These important Vector Algebra questions cover high-weightage concepts from Vectors and scalars, the addition of vectors, Components of a vector in two dimensions and three-dimensional spaces, Scalar and vector products — the topics JEE repeats every year.

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Q1MathsUnit 12: Vector Algebra

An airplane is heading north east at a speed of

141 m s^{-1}

. The northward component of its velocity is:

Q2MathsUnit 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

Q3MathsUnit 12: Vector Algebra

Let

\mathrm{ABC}

be a triangle and let

\mathrm{S}

be its circumcentre and

\mathrm{O}

be its orthocentre. The

\overline{\mathbf{S A}}+\overline{\mathbf{S B}}+\overline{\mathbf{S C}}=

Q4MathsUnit 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}

Q5MathsUnit 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

Q6MathsUnit 12: Vector Algebra

Six vectors, a through f have the magnitudes and directions indicated in the figure. Which of the following statements is true?

Q7MathsUnit 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 :

Q8MathsUnit 12: Vector Algebra

A zero vector has

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Frequently asked questions

What makes a Vector Algebra question "important" for JEE?

Important questions test core concepts that appear frequently across JEE Main and Advanced papers — definitions, standard formulas, and classic problem types.

Which subtopics in Vector Algebra are high-weightage?

Key areas include Vectors and scalars, the addition of vectors, Components of a vector in two dimensions and three-dimensional spaces, Scalar and vector products. Prioritise these before moving to edge cases.

How many important questions should I revise?

Revise 30–50 important MCQs per unit in the last month before JEE. Focus on questions you got wrong at least once.

Can I practise only important questions on Goodmarks?

Pro users can filter by unit and subtopic to target high-yield areas. Free users can attempt sample questions on this page.