vectors-m

Related Questions

• Let $\alpha ,\,\,\beta ,\,\,\gamma $ be distinct real numbers. The points with position vectors $\alpha \mathbf{i}+\beta \mathbf{j}+\gamma \mathbf{k},\,\,\beta \mathbf{i}+\gamma \mathbf{j}+\alpha \mathbf{k},\,\,\gamma \mathbf{i}+\alpha \mathbf{j}+\beta \mathbf{k}$

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• If the position vectors of the vertices of a triangle be $2\mathbf{i}+4\mathbf{j}-\mathbf{k},$ $4\mathbf{i}+5\mathbf{j}+\mathbf{k}$ and $3\mathbf{i}+6\mathbf{j}-3\mathbf{k},$ then the triangle is

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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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• The position vector of the points which divides internally in the ratio 2 : 3 the join of the points $2\mathbf{a}-3\mathbf{b}$ and $3\mathbf{a}-2\mathbf{b},$ is

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• The area of the parallelogram whose diagonals are $\mathbf{a}=3\,\mathbf{i}+\mathbf{j}-2\mathbf{k}$ and $\mathbf{b}=\mathbf{i}-3\,\mathbf{j}+4\,\mathbf{k}$ is

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