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Scalar and vector products Revision for JEE

14+ syllabus-aligned questions available

Quick answer

Revise Scalar and vector products by covering every subtopic once, drilling formulas, then solving 14+ timed MCQs with full solutions.

Use this Scalar and vector products revision checklist before mocks and the final exam. Reinforce concepts with 14+ syllabus-aligned MCQs on Goodmarks.

Revision checklist

  1. 1.Core idea: Scalar and vector products
  2. 2.Relates to other subtopics in Vector Algebra
  3. 3.Vector components in 2D and 3D
  4. 4.Scalar and vector products
  5. 5.Master Scalar and vector products definitions and standard results
  6. 6.Solve 20 timed MCQs for Scalar and vector products

Syllabus context

Part of Vector Algebra in JEE Main Mathematics.

Free sample questions

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Q1MathsUnit 12: Vector Algebra
Let a,β,γa, \beta, \gamma be distinct real numbers. The points with position vectors ai +βj++\beta j+ γk,βi+γj+ak,γi+aj+βk\gamma k, \beta i+\gamma j+a k, \gamma i+a j+\beta k
Q2MathsUnit 12: Vector Algebra
The non zero vector a⃗,b⃗,c⃗\vec{a}, \vec{b}, \vec{c} related by a⃗=8b⃗\vec{a}=8 \vec{b} and c⃗=−7b⃗,\vec{c}=-7 \vec{b}, then angle between a⃗&c⃗\vec{a} \& \vec{c} is
Q3MathsUnit 12: Vector Algebra
Consider ΔABC\Delta A B C with A≡(a⃗),B≡(b⃗)A \equiv(\vec{a}), B \equiv(\vec{b}) and C=(c⃗),C=(\vec{c}), ff b⃗.(a⃗+c⃗)=b⃗⋅b⃗+\vec{b} .(\vec{a}+\vec{c})=\vec{b} \cdot \vec{b}+ a⃗⋅c⃗;∣b⃗−a⃗∣=3;∣c⃗−b⃗∣=4\vec{a} \cdot \vec{c} ;|\vec{b}-\vec{a}|=3 ;|\vec{c}-\vec{b}|=4 then the angle between the medians AM‾\overline{A M} and BDB D is
Q4MathsUnit 12: Vector Algebra
For any four points P,Q,R,SP, Q, R, S ∣PQ→×R→S−QR→×P→S+R→P×Q→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
If a,b,ca, b, c are non-coplanar vectors and λ\lambda is a real number, then [λ(a⃗+b⃗)λ2b⃗λc⃗]=[a⃗b⃗+c⃗b⃗]\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)A(-1,3,0), B(2,2,1) and C(1,1,3)C(1,1,3) determine a plane. The distance of the plane A,B,CA, B, C from the point D(5,7,8)D(5,7,8) is
Q7MathsUnit 12: Vector Algebra
The vectors i^+2j^+3k^,2i^−j^+k^\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 3i^+j^+4k^\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
If V⃗=3i^+4j^\vec{V}=3 \hat{i}+4 \hat{j} then, with what scalar 'C must it be multiplied so that C∣V→∣=C|\overrightarrow{\boldsymbol{V}}|= 7.5:\mathbf{7 . 5}:

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How should I revise Scalar and vector products before JEE?

Follow the checklist on this page, revise formulas daily, and attempt mixed MCQs every 2–3 days.

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