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Question

ifa,b andc are three unit vector a is perpendicular to b and c and angle between b and cb is30, prove that a=±2(b×c).

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Solution

Given
¯¯¯a=1,¯¯b=1,¯¯c=1¯¯¯ais12to¯¯b,¯¯c,(¯¯b¯¯c)=300Toprove¯¯¯a=±2(¯¯bׯ¯c)Weknow¯¯bׯ¯cis12to¯¯b,¯¯c¯¯¯aand¯¯bׯ¯careparallol¯¯¯a=±(¯¯bׯ¯c)1ttScales¯¯¯a=|t|(¯¯bׯ¯c)1=|t|¯¯b¯¯cin(¯¯¯a¯¯c)1=|t|x1×1sin300|t|=2to±2in1¯¯¯a=±2(¯¯bׯ¯c)

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