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Hard Components of a vector in two dimensions and three-dimensional spaces MCQs for JEE

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Hard Components of a vector in two dimensions and three-dimensional spaces MCQs train multi-concept problem solving — attempt after mastering easy and medium sets (2+ on Goodmarks).

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Part of Vector Algebra in JEE Main Mathematics.

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Q1MathsUnit 12: Vector Algebra
An airplane is heading north east at a speed of 141ms−1141 m s^{-1}. The northward component of its velocity is:
Q2MathsUnit 12: Vector Algebra
Let α,β,γ\alpha, \beta, \gamma be the distinct real numbers. The vectors αi^+βj^+rk^\boldsymbol{\alpha} \hat{\boldsymbol{i}}+\boldsymbol{\beta} \hat{\boldsymbol{j}}+\boldsymbol{r} \hat{\boldsymbol{k}} βi^+rj^+αk^;γi^+αj^+βk^\beta \hat{i}+r \hat{j}+\alpha \hat{k} ; \gamma \hat{i}+\alpha \hat{j}+\beta \hat{k} are

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