Mathematics in Physics

JEE Main level, single correct, medium

49 of 121

Question 49 of 121

What will be the projection of vector A⃗=i^+j^+k^\vec{A}=\hat{i}+\hat{j}+\hat{k} on vector B⃗=i^+j^?\vec{B}=\hat{i}+\hat{j}?

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Answer: (D) (i^+j^)(\hat{i}+\hat{j})

(Acos⁡θ)B^=A(A⃗⋅B⃗AB)B^=A⃗⋅B⃗BB^\left(A\cos \theta \right)\hat{B}=A\left(\dfrac{\vec{A}\cdot \vec{B}}{AB}\right)\hat{B}=\dfrac{\vec{A}\cdot \vec{B}}{B}\hat{B}
=22(i^+j^2)=i^+j^=\dfrac{2}{\sqrt{2}}\left(\dfrac{\hat{i}+\hat{j}}{\sqrt{2}}\right)=\hat{i}+\hat{j}

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