Vector equation of the plane in the scalar dot product form is

MATHEMATICS · Single correct · IB Diploma Programme · Mathematics: Analysis and Approaches · Geometry and Trigonometry · Geometry and Trigonometry

Problem

Vector equation of the plane r=i−j+λ(i+j+k)+μ(i−2j+3k)\mathbf{r} = \mathbf{i} - \mathbf{j} + \lambda(\mathbf{i} + \mathbf{j} + \mathbf{k}) + \mu(\mathbf{i} - 2\mathbf{j} + 3\mathbf{k}) in the scalar dot product form is (1) r⋅(5i−2j+3k)=7\mathbf{r} \cdot (5\mathbf{i} - 2\mathbf{j} + 3\mathbf{k}) = 7 (2) r⋅(5i+2j−3k)=7\mathbf{r} \cdot (5\mathbf{i} + 2\mathbf{j} - 3\mathbf{k}) = 7 (3) r⋅(5i−2j−3k)=7\mathbf{r} \cdot (5\mathbf{i} - 2\mathbf{j} - 3\mathbf{k}) = 7 (4) r⋅(5i+2j+3k)=7\mathbf{r} \cdot (5\mathbf{i} + 2\mathbf{j} + 3\mathbf{k}) = 7

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