Let <span class="math-tex">\(\rm \vec a =\hat i +\hat j +\hat k,\; \vec b =\hat i -\hat j + \hat k\)</span> and c = î - ĵ - k̂ be three vectors. A vector <span class="math-tex">\(\rm \vec v\)</span> in the plane of <span class="math-tex">\(\rm \vec a\)</span> and <span class="math-tex">\(\rm \vec b\)</span> whose projection on <span class="math-tex">\(\rm \frac {\vec c} {|\vec c|}\)</span> is <span class="math-tex">\(\frac 1 {\sqrt 3},\)</span> is
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