vectors-m

Related Questions

• A vector of length 3 perpendicular to each of the vectors $3\,\mathbf{i}+\mathbf{j}-4\,\mathbf{k}$ and $6\,\mathbf{i}+5\,\mathbf{j}-2\,\mathbf{k}$ is

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• If A, B, C, D are any four points in space, then $|\overrightarrow{AB}\times \overrightarrow{CD}+\overrightarrow{BC}\times \overrightarrow{AD}+\overrightarrow{CA}\times \overrightarrow{BD}|$ is equal to (where $\Delta$ denotes the area of $\Delta ABC$)

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• If $\mathbf{a}, \mathbf{b}, \mathbf{c}$, are three non-coplanar vectors such that $\mathbf{a}+\mathbf{b}+\mathbf{c}=\alpha \,\mathbf{d}$ and $\mathbf{b}+\mathbf{c}+\mathbf{d}=\beta \,\mathbf{a},$ then $\mathbf{a}+\mathbf{b}+\mathbf{c}+\mathbf{d}$ is equal to

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• A unit vector in the $xy-$plane which is perpendicular to $4\mathbf{i}-3\mathbf{j}+\mathbf{k}$ is

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• If $\overrightarrow{{{F}_{1}}}=\mathbf{i}-\mathbf{j}+\mathbf{k},$ $\overrightarrow{{{F}_{2}}}=-\mathbf{i}+2\mathbf{j}-\mathbf{k},$ $\overrightarrow{{{F}_{3}}}=\mathbf{j}-\mathbf{k},$ $\vec{A}=4\mathbf{i}-3\mathbf{j}-2\mathbf{k}$ and $\vec{B}=6\mathbf{i}+\mathbf{j}-3\mathbf{k},$ then the scalar product of $\overrightarrow{{{F}_{1}}}+\overrightarrow{{{F}_{2}}}+\overrightarrow{{{F}_{3}}}$and $\overrightarrow{AB}$ will be

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