vectors-m

Related Questions

• 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

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• The direction cosines of vector $\mathbf{a}=3\mathbf{i}+4\mathbf{j}+5\mathbf{k}$ in the direction of positive axis of x, 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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• $\mathbf{a},\,\mathbf{b}$ and c are three vectors with magnitude $|\mathbf{a}|\,=4,$ $|\mathbf{b}|\,=4,$ $|\mathbf{c}|\,=2$ and such that $\mathbf{a}$ is perpendicular to $(\mathbf{b}+\mathbf{c}),\,\mathbf{b}$ is perpendicular to $(\mathbf{c}+\mathbf{a})$ and $\mathbf{c}$ is perpendicular to $(\mathbf{a}+\mathbf{b}).$ It follows that $|\mathbf{a}+\mathbf{b}+\mathbf{c}|$ is equal to

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• If $\theta$ be the angle between the unit vectors a and b, then $\mathbf{a}-\sqrt{2}\,\mathbf{b}$ will be a unit vector if $\theta =$

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