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Mathematics · JEE

Scalar and vector products Short Tricks for JEE

14+ syllabus-aligned questions available

Quick answer

Short tricks for Scalar and vector products work only with strong fundamentals. Apply the tips below in timed sets and review every explanation.

Use these Scalar and vector products shortcuts to save time in JEE Mathematics papers — then validate speed with 14+ MCQs on Goodmarks.

Short tricks for speed

  • Scalar and vector products focus drill

    Solve 15 mixed MCQs for Scalar and vector products, review every explanation, and note formulas you hesitated on.

  • Calculus substitution scan

    Spot standard forms (sin²x, 1/(a²+x²), e^ax) before integrating — JEE rewards pattern recognition.

  • Graph sketch shortcut

    For coordinate geometry, mark intercepts and asymptotes first; many MCQs need only qualitative graph features.

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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Frequently asked questions

Are short tricks enough for Scalar and vector products in JEE?

No — tricks complement concepts. Master the theory first, then use shortcuts in timed MCQ practice.

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