Скачать или смотреть â, b̂ and ĉ are unit vectors, â.b̂ = â.ĉ = 0 and angle between b̂ and ĉ is π/6,P.T. â = ±2 (b̂ × ĉ)

If â, b̂ and ĉ are unit vectors such that â.b̂ = â.ĉ = 0 and the angle
between b̂ and ĉ is π/6 , then prove that â = ±2 (b̂ × ĉ)


cbse 12th maths old board exam question paper 2024 2025 supplementary vector algebra perpendicular vectors condition


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This video explains a fundamental vector algebra result that appears repeatedly across mathematics and physics syllabi from secondary education to undergraduate level. The problem connects unit vectors orthogonality and geometric interpretation of the cross product. When vector a is perpendicular to both vector b and vector c and the angle between b and c is pi by six the relationship a equals plus or minus two times the cross product of b and c follows directly from vector magnitude and direction principles.

Such questions are commonly tested in vector chapters under three dimensional geometry mechanics and electromagnetic theory. Students encounter this concept while studying advanced school mathematics physics with calculus engineering mathematics and introductory linear algebra. It also appears in structured proof questions and application based problems in entrance examinations and university assessments where understanding vector orientation is essential.

The solution builds on properties of unit vectors dot product equals zero implying perpendicularity and the magnitude of the cross product depending on sine of the included angle. Since the sine of pi by six is one by two the magnitude becomes exactly one half which explains the factor of two in the final expression. The plus or minus sign comes from direction and orientation which is often emphasized in marking schemes.

This exact reasoning has appeared in previous question papers framed in different formats such as proving a given identity finding magnitude or verifying direction. It is taught in higher secondary mathematics under vector algebra modules and later revisited in physics topics like magnetic force rotational motion and rigid body dynamics. Courses following structured international mathematics programs and standardized entrance tests expect students to clearly justify each step using vector identities rather than memorized formulas.

This explanation aligns with how examiners expect answers to be written with logical flow clear justification and correct use of vector notation. It helps learners preparing for school final exams competitive engineering and medical entrance tests undergraduate physics and mathematics courses and standardized aptitude assessments where vector reasoning is frequently tested.

Watching this video strengthens conceptual understanding and reduces errors related to sign ambiguity magnitude calculation and geometric interpretation. It is especially useful for students revising vectors across multiple subjects since the same identity appears in different contexts with different wording. By mastering this proof learners gain confidence to handle a wide range of vector problems asked across curricula and examinations worldwide.

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