vectors-m

Related Questions

• If $(x,\,\,y,\,\,z)\ne (0,\,\,0,\,\,0)$ and $(\mathbf{i}+\mathbf{j}+3\,\mathbf{k})\,x+(3\,\mathbf{i}-3\mathbf{j}+\mathbf{k})\,y$ $+(-4\mathbf{i}+5\mathbf{j})\,z=\lambda \,(x\mathbf{i}+y\mathbf{j}+z\mathbf{k}),$ then the value of $\lambda$ will be

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• If the vectors $a\,\mathbf{i}-2\mathbf{j}+3\mathbf{k}$ and $3\mathbf{i}+6\mathbf{j}-5\mathbf{k}$ are perpendicular to each other, then a is given by

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• 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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• 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 $\mathbf{a}=2\mathbf{i}+3\mathbf{j}-5\mathbf{k},\,\,\mathbf{b}=m\mathbf{i}+n\mathbf{j}+12\mathbf{k}$ and $\mathbf{a}\times \mathbf{b}=0,$ then $(m,\,\,n)=$

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