Questions in vectors-m

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If $\mathbf{a}=\mathbf{i}+\mathbf{j}+\mathbf{k},\,\mathbf{b}=\mathbf{i}+3\mathbf{j}+5\mathbf{k}$ and $\mathbf{c}=7\mathbf{i}+9\mathbf{j}+11\mathbf{k}$, then the area of the parallelogram having diagonals a + b and b + c is
The area of the parallelogram whose diagonals are $\frac{3}{2}\mathbf{i}+\frac{1}{2}\mathbf{j}-\mathbf{k}$ and $2\mathbf{i}-6\mathbf{j}+8\mathbf{k}$ is
The area of the triangle having vertices as $\mathbf{i}-2\mathbf{j}+3\mathbf{k},$ $\,-2\mathbf{i}+3\mathbf{j}+\mathbf{k}$ , $4\mathbf{i}-7\mathbf{j}+7\mathbf{k}$ is
The area of the parallelogram whose adjacent sides are $\mathbf{i}-\mathbf{k}$ and $2\mathbf{j}+3\mathbf{k}$ is
The moment of the force $\overrightarrow{F}$ acting at a point P, about the point C is
Three forces $\mathbf{i}+2\,\mathbf{j}-3\,\mathbf{k},\,\,2\,\mathbf{i}+3\,\mathbf{j}+4\,\mathbf{k}$ and $\mathbf{i}-\mathbf{j}+\mathbf{k}$ are acting on a particle at the point (0, 1, 2). The magnitude of the moment of the forces about the point $(1,\,-2,\,0)$ is
Let the points A, B and P be (– 2, 2, 4), (2, 6, 3) and (1,2,1) respectively. The magnitude of the moment of the force represented by $\overrightarrow{AB}$ and acting at A about P is
The moment of a force represented by $\overrightarrow{F}=\mathbf{i}+2\mathbf{j}+3\mathbf{k}$ about the point $2\,\mathbf{i}-\mathbf{j}+\mathbf{k}=$
A force of magnitude 6 acts along the vector $(9,\,6,\,-2)$ and passes through a point A (4, – 1, –7). The moment of the force about the point O (1, – 3, 2) is
A force $\mathbf{F}=2\mathbf{i}+\mathbf{j}-\mathbf{k}$ acts at a point A, whose position vector is $2\mathbf{i}-\mathbf{j}$. The moment of F about the origin is

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