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If $\overrightarrow{OA}=3\mathbf{i}+2\mathbf{j}-\mathbf{k}$ and $\overrightarrow{OB}=\mathbf{i}+3\mathbf{j}+\mathbf{k}$, then the area of the triangle OAB is
Let a, b, c be the position vectors of the vertices of a triangle ABC. The vector area of triangle ABC is
If $|\mathbf{a}|\,=2,\,\,|\mathbf{b}|\,=3$ and a, b are mutually perpendicular, then the area of the triangle whose vertices are $\mathbf{0},\,\,\mathbf{a}+\mathbf{b},\,\,\mathbf{a}-\mathbf{b}$ is
If $\mathbf{i}+2\mathbf{j}+3\mathbf{k}$ and $3\mathbf{i}-2\mathbf{j}+\mathbf{k}$ represents the adjacent sides of a parallelogram, then the area of this parallelogram is
If $3\mathbf{i}+4\mathbf{j}$ and $-5\mathbf{i}+7\mathbf{j}$ are the vector sides of any triangle, then its area is given by
If the vectors $\mathbf{i}-3\mathbf{j}+2\mathbf{k}$, $-\mathbf{i}+2\mathbf{j}$ represents the diagonals of a parallelogram, then its area will be
The area of the parallelogram whose diagonals are the vectors $2\mathbf{a}-\mathbf{b}$ and $4\mathbf{a}-5\mathbf{b},$ where a and b are the unit vectors forming an angle of ${{45}^{o}},$ is
The area of a parallelogram whose adjacent sides are $\mathbf{i}-2\mathbf{j}+3\mathbf{k}$ and $2\mathbf{i}+\mathbf{j}-4\mathbf{k},$ is
If the diagonals of a parallelogram are represented by the vectors $3\mathbf{i}+\mathbf{j}-2\mathbf{k}$ and $\mathbf{i}+3\mathbf{j}-4\mathbf{k},$ then its area in square unit is
The area of a parallelogram whose adjacent sides are given by the vectors $\mathbf{i}+2\mathbf{j}+3\mathbf{k}$ and $-3\mathbf{i}-2\mathbf{j}+\mathbf{k}$ (in square unit) is

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