The 3-dimensional vectors satisfying

MATHEMATICS · Single correct · CBSE · Mathematics · Vector Algebra · Vector Algebra

Problem

The 3-dimensional vectors v1,v2,v3\mathbf{v}_1, \mathbf{v}_2, \mathbf{v}_3 satisfying v1⋅v1=4,v1⋅v2=−2,v1⋅v3=6,v2⋅v2=2,v2⋅v3=−5,v3⋅v3=29\mathbf{v}_1 \cdot \mathbf{v}_1 = 4, \mathbf{v}_1 \cdot \mathbf{v}_2 = -2, \mathbf{v}_1 \cdot \mathbf{v}_3 = 6, \mathbf{v}_2 \cdot \mathbf{v}_2 = 2, \mathbf{v}_2 \cdot \mathbf{v}_3 = -5, \mathbf{v}_3 \cdot \mathbf{v}_3 = 29 , then v3\mathbf{v}_3 may be (1) −3i^+2j^±4k^-3\hat{i} + 2\hat{j} \pm 4\hat{k} (2) 3i^−2j^±4k^3\hat{i} - 2\hat{j} \pm 4\hat{k} (3) −2i^+3j^±4k^-2\hat{i} + 3\hat{j} \pm 4\hat{k} (4) 2i^+3j^±4k^2\hat{i} + 3\hat{j} \pm 4\hat{k}

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