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Question Number 18094 by Tinkutara last updated on 15/Jul/17

$$\overrightarrow{A},\overrightarrow{B}\mathrm{and}\overrightarrow{C}\mathrm{are}\mathrm{three}\mathrm{non}-\mathrm{collinear},$$$$\mathrm{non}\mathrm{co}-\mathrm{planar}\mathrm{vectors}.\mathrm{What}\mathrm{can}\mathrm{you}$$$$\mathrm{say}\mathrm{about}\mathrm{direction}\mathrm{of}\overrightarrow{A}\times \left(\overrightarrow{B}\times \overrightarrow{C}\right)?$$

Commented by ajfour last updated on 15/Jul/17

$$\overrightarrow{\mathrm{A}}\times \left(\overrightarrow{\mathrm{B}}\times \overrightarrow{\mathrm{C}}\right)\mathrm{is}\mathrm{the}\mathrm{cross}\mathrm{product}\mathrm{of}$$$$\mathrm{the}\mathrm{component}\mathrm{of}\overrightarrow{\mathrm{A}}\mathrm{in}\mathrm{the}\mathrm{plane}$$$$\mathrm{of}\overrightarrow{\mathrm{B}}\mathrm{and}\overrightarrow{\mathrm{C}}\mathrm{with}\overrightarrow{\mathrm{B}}\times \overrightarrow{\mathrm{C}}.$$$$\mathrm{It}\mathrm{is}\mathrm{parallel}\mathrm{to}\mathrm{the}\mathrm{plane}\mathrm{of}\overrightarrow{\mathrm{B}}\mathrm{and}\overrightarrow{\mathrm{C}}.$$

Commented by ajfour last updated on 15/Jul/17

Commented by Tinkutara last updated on 15/Jul/17

$$\mathrm{Thanks}\mathrm{Sir}!$$

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