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Question Number 91496 by Zainal Arifin last updated on 01/May/20

$$\mathrm{The}\mathrm{vector}\mathbf{a}=3\mathbf{i}-2\mathbf{j}+2\mathbf{k}\mathrm{and}\mathbf{b}=-\mathbf{i}-2\mathbf{k}$$$$\mathrm{are}\mathrm{the}\mathrm{adjacent}\mathrm{sides}\mathrm{of}\mathrm{a}\mathrm{parallelogram}.$$$$\mathrm{Then}\mathrm{angle}\mathrm{between}\mathrm{its}\mathrm{diagonal}\mathrm{is}$$

Commented by jagoll last updated on 01/May/20

$$\overrightarrow{a}+\overrightarrow{b}=(2,-2,0)$$$$\overrightarrow{a}-\overrightarrow{b}=(4,-2,4)$$$$let\theta =theanglebetweendiagonals$$$$\cos \theta =\frac{8+4}{2\sqrt{2}.6}=\frac{1}{\sqrt{2}}\Rightarrow \theta =\frac{\pi }{4}$$

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