Consider two vectors u=3i-j and v=2i+j-, λ > 0. The angle between them is given by cos ⁻¹ ((√(5))/(2√(7))). Let v=v₁+v₂, where v₁ is parallel to u and v₂ is perpendicular to u. Then the value of |v₁|² + |v₂|² is:

Vector Algebra: JEE Main 2025 Mathematics question

JEE Main 2025 · April, Unspecified (session-level dataset) · Q139

JEE Main 2025April, Unspecified (session-level dataset)MathematicsMediumVector Algebra184× since 2002

Consider two vectors \mathbf{u}=3\mathbf{i}-\mathbf{j} and \mathbf{v}=2\mathbf{i}+\mathbf{j}-\lambda\mathbf{k}, \lambda > 0. The angle between them is given by \cos⁻¹\bigl(\tfrac{\sqrt{5}}{2\sqrt{7}}\bigr). Let \mathbf{v}=\mathbf{v}_1+\mathbf{v}_2, where \mathbf{v}_1 is parallel to \mathbf{u} and \mathbf{v}_2 is perpendicular to \mathbf{u}. Then the value of |\mathbf{v}_1|² + |\mathbf{v}_2|² is:

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JEE Main 2025 Vector Algebra Question with Solution (April Unspecified (session-level dataset), Q139) | JEE Arc

Vector Algebra: JEE Main 2025 Mathematics question

JEE Main 2025 · April, Unspecified (session-level dataset) · Q139

JEE Main 2025April, Unspecified (session-level dataset)MathematicsMediumVector Algebra184× since 2002

More on Vector Algebra

Practise this topic