The vector <span class="math-tex">\(\vec{a}=α \hat{i}+2\hat{j}+β \hat{k}\)</span> lies in the plane of the vector <span class="math-tex">\(\vec{b}=\hat{i} + \hat{j}\)</span> and <span class="math-tex">\(\vec{c}=\hat{j} + \hat{k}\)</span> and bisects the angle between <span class="math-tex">\(\vec{b}\)</span> and <span class="math-tex">\(\vec{c}\)</span>. Then, which one of the following gives possible values of α and β ?
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