Mathematics · JEE

Important Questions: Scalar and vector products for JEE

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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}})

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What makes a Scalar and vector products 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 Scalar and vector products. Prioritise these before moving to edge cases.

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

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