Questions in vectors-m

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If the position vectors of A and B be $6\mathbf{i}+\mathbf{j}-3\mathbf{k}$ and $4\mathbf{i}-3\mathbf{j}-2\mathbf{k},$ then the work done by the force $\vec{B}=\mathbf{i}+\mathbf{j}+5\mathbf{k}$ in displacing a particle from A to B is
If the force $\overrightarrow{F}=\mathbf{i}+2\mathbf{j}+3\mathbf{k}$ moves from $\mathbf{i}+\mathbf{j}-\mathbf{k}$ to $2\mathbf{i}-\mathbf{j}+\mathbf{k},$ then work done will be represented by
The work done by the force $F=2\mathbf{i}-3\mathbf{j}+2\mathbf{k}$ in displacing a particle from the point (3, 4, 5) to the point (1, 2, 3) is
Force $3\mathbf{i}+2\mathbf{j}+5\mathbf{k}$ and $2\mathbf{i}+\mathbf{j}-3\mathbf{k}$ are acting on a particle and displace it from the point $2\mathbf{i}-\mathbf{j}-3\mathbf{k}$ to the point $4\mathbf{i}-3\mathbf{j}+7\mathbf{k},$ then work done by the force is
A particle acted on by two forces $3\mathbf{i}+2\mathbf{j}-3\mathbf{k}$ and $2\mathbf{i}+4\mathbf{j}+2\mathbf{k}$ is displaced from the point $\mathbf{i}+2\mathbf{j}+\mathbf{k}$ to $5\mathbf{i}+4\mathbf{j}+2\mathbf{k}.$ The total work done by the forces is equal to
The work done in moving an object along the vector $3\mathbf{i}+2\mathbf{j}-5\mathbf{k},$ if the applied force is $\overrightarrow{F}=2\mathbf{i}-\mathbf{j}-\mathbf{k}$, is
A force of magnitude 5 units acting along the vector $2i-2j+k$ displaces the point of application from $(1,\,2,\,3)$ to $\mathbf{a}\times \mathbf{b}=\mathbf{b}\times \mathbf{c}\ne \mathbf{0}$, then the work done is
A particle acted on by constant forces $4i+j-3k$ and $3i+j-k$ is displaced from the point $i+2j+3k$ to the point $5i+4j+k$. The total work done by the force is
If the scalar projection of the vectors $x\mathbf{i}-\mathbf{j}+\mathbf{k}$on the vector $2\mathbf{i}-\mathbf{j}+5\mathbf{k}$ is $\frac{1}{\sqrt{30}}$then value of x is equal to
If $\mathbf{x}+\mathbf{y}+\mathbf{z}=0,|\mathbf{x}|=|\mathbf{y}|=|\mathbf{z}|=2$ and $\theta $ is angle between $\mathbf{y}$ and $\mathbf{z}$, then the value of $\text{cose}{{\text{c}}^{2}}\theta +{{\cot }^{2}}\theta $ is equal to

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