JEE Main 20264 Apr, Morning shiftMathematicsMediumVector Algebra184× since 2002Let a⃗k=(tanθk)i^+j^\vec{a}_k=(\tan\theta_k)\hat{i}+\hat{j}ak=(tanθk)i^+j^ and b⃗k=i^−(cotθk)j^\vec{b}_k=\hat{i}-(\cot\theta_k)\hat{j}bk=i^−(cotθk)j^, where θk=2k−1π2n+1\theta_k=\frac{2^{k-1}\pi}{2^n+1}θk=2n+12k−1π, for some n∈Nn\in\mathbb{N}n∈N, n>5n>5n>5. Then the value of ∑k=1n∣a⃗k∣2∑k=1n∣b⃗k∣2\frac{\sum_{k=1}^{n}|\vec{a}_k|^2}{\sum_{k=1}^{n}|\vec{b}_k|^2}∑k=1n∣bk∣2∑k=1n∣ak∣2 is ______.Your answerType your answer. Integers and decimals are accepted.CheckSkip · show solution
