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The 3-dimensional vectors satisfying
MATHEMATICS · Single correct · CBSE · Mathematics · Vector Algebra · Vector Algebra
Problem The 3-dimensional vectors v 1 , v 2 , v 3 \mathbf{v}_1, \mathbf{v}_2, \mathbf{v}_3 v 1 , v 2 , v 3 satisfying v 1 ⋅ v 1 = 4 , v 1 ⋅ v 2 = − 2 , v 1 ⋅ v 3 = 6 , v 2 ⋅ v 2 = 2 , v 2 ⋅ v 3 = − 5 , v 3 ⋅ v 3 = 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 v 1 ⋅ v 1 = 4 , v 1 ⋅ v 2 = − 2 , v 1 ⋅ v 3 = 6 , v 2 ⋅ v 2 = 2 , v 2 ⋅ v 3 = − 5 , v 3 ⋅ v 3 = 29 , then v 3 \mathbf{v}_3 v 3 may be
(1) − 3 i ^ + 2 j ^ ± 4 k ^ -3\hat{i} + 2\hat{j} \pm 4\hat{k} − 3 i ^ + 2 j ^ ± 4 k ^
(2) 3 i ^ − 2 j ^ ± 4 k ^ 3\hat{i} - 2\hat{j} \pm 4\hat{k} 3 i ^ − 2 j ^ ± 4 k ^
(3) − 2 i ^ + 3 j ^ ± 4 k ^ -2\hat{i} + 3\hat{j} \pm 4\hat{k} − 2 i ^ + 3 j ^ ± 4 k ^
(4) 2 i ^ + 3 j ^ ± 4 k ^ 2\hat{i} + 3\hat{j} \pm 4\hat{k} 2 i ^ + 3 j ^ ± 4 k ^
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