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If-three-vector-a-b-and-c-are-such-that-a-0-and-a-b-2-a-c-a-c-1-b-4-and-the-angle-between-b-and-c-is-cos-1-1-4-then-b-2c-




Question Number 140502 by benjo_mathlover last updated on 08/May/21
If three vector a^→  , b^→  and c^→  are   such that a^→  ≠ 0 and a^→ ×b^→  = 2(a^→ ×c^→ )  ,∣a^→ ∣ = ∣c^→ ∣ = 1 , ∣b^→ ∣ = 4 and the   angle between b^→  and c^→  is cos^(−1) ((1/4)),  then b^→ −2c^→  = λ a^→ , where λ =?
$$\mathrm{If}\:\mathrm{three}\:\mathrm{vector}\:\overset{\rightarrow} {\mathrm{a}}\:,\:\overset{\rightarrow} {\mathrm{b}}\:\mathrm{and}\:\overset{\rightarrow} {\mathrm{c}}\:\mathrm{are}\: \\ $$$$\mathrm{such}\:\mathrm{that}\:\overset{\rightarrow} {\mathrm{a}}\:\neq\:\mathrm{0}\:\mathrm{and}\:\overset{\rightarrow} {\mathrm{a}}×\overset{\rightarrow} {\mathrm{b}}\:=\:\mathrm{2}\left(\overset{\rightarrow} {\mathrm{a}}×\overset{\rightarrow} {\mathrm{c}}\right) \\ $$$$,\mid\overset{\rightarrow} {\mathrm{a}}\mid\:=\:\mid\overset{\rightarrow} {\mathrm{c}}\mid\:=\:\mathrm{1}\:,\:\mid\overset{\rightarrow} {\mathrm{b}}\mid\:=\:\mathrm{4}\:\mathrm{and}\:\mathrm{the}\: \\ $$$$\mathrm{angle}\:\mathrm{between}\:\overset{\rightarrow} {\mathrm{b}}\:\mathrm{and}\:\overset{\rightarrow} {\mathrm{c}}\:\mathrm{is}\:\mathrm{cos}^{−\mathrm{1}} \left(\frac{\mathrm{1}}{\mathrm{4}}\right), \\ $$$$\mathrm{then}\:\overset{\rightarrow} {\mathrm{b}}−\mathrm{2}\overset{\rightarrow} {\mathrm{c}}\:=\:\lambda\:\overset{\rightarrow} {\mathrm{a}},\:\mathrm{where}\:\lambda\:=? \\ $$

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