vectors-m

Related Questions

• Let $\mathbf{a},\,\mathbf{b},\,\mathbf{c}$ be three vectors such that $\mathbf{a}\ne 0,$ and $\mathbf{a}\times \mathbf{b}=2\mathbf{a}\times \mathbf{c},\,\,|\mathbf{a}|\,=\,|\mathbf{c}|\,=\,1,\,|\mathbf{b}|\,=4$ and $|\mathbf{b}\times \mathbf{c}|\,=15.$ If $\mathbf{b}-2\mathbf{c}=\lambda \mathbf{a},$ then $\lambda$ equals to

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• If $|\mathbf{a}|=|\mathbf{b}|=1$ and $\mathbf{|a}+\mathbf{b}|=\sqrt{3}$, then the value of $(3\mathbf{a}-4\mathbf{b}).(2\mathbf{a}+5\mathbf{b})$ is

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• If ABCDEF is a regular hexagon and $\overrightarrow{AB}+\overrightarrow{AC}+\overrightarrow{AD}+\overrightarrow{AE}+\overrightarrow{AF}=\lambda \,\overrightarrow{AD},$ then $\lambda =$

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• The position vector of vertices of a triangle ABC are $4\mathbf{i}-2\mathbf{j},\,\mathbf{i}+4\mathbf{j}-3\mathbf{k}$ and $-\mathbf{i}+5\mathbf{j}+\mathbf{k}$ respectively, then $\angle ABC=$

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• The unit vector perpendicular to both $\mathbf{i}+\mathbf{j}$ and $\mathbf{j}+\mathbf{k}$ is

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