vectors-m

Related Questions

• If $\mathbf{a}=2\mathbf{i}+5\mathbf{j}$ and $\mathbf{b}=2\mathbf{i}-\mathbf{j},$ then the unit vector along $y=0$ will be

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• For any three non-zero vectors ${{r}_{1}},\,{{r}_{2}}$ and ${{r}_{3}}$, $\begin{vmatrix} {{r}_{1}}\,.\,{{r}_{1}} & {{r}_{1}}\,.\,{{r}_{2}} & {{r}_{1}}\,.\,{{r}_{3}} \\ {{r}_{2}}\,.\,{{r}_{1}} & {{r}_{2}}\,.\,{{r}_{2}} & {{r}_{2}}\,.\,{{r}_{3}} \\ {{r}_{3}}\,.\,{{r}_{1}} & {{r}_{3}}\,.\,{{r}_{2}} & {{r}_{3}}\,.\,{{r}_{3}} \\ \end{vmatrix}=0$. Then which of the following is false

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• 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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• The area of a parallelogram whose adjacent sides are given by the vectors $\mathbf{i}+2\mathbf{j}+3\mathbf{k}$ and $-3\mathbf{i}-2\mathbf{j}+\mathbf{k}$ (in square unit) is

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• If $\mathbf{a}+\mathbf{b}+\mathbf{c}=\mathbf{0},$ then which relation is correct

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