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If veca , vecb , vecc and vecd are four ...

If `veca , vecb , vecc and vecd` are four non-coplanar unit vectors such that `vecd` makes equal angles with all the three vectors `veca, vecb, vecc` then prove that `[vecd vecavecb]=[vecd veccvecb]=[vecd veccveca]`

Text Solution

Verified by Experts

Since `vecd` makes equalw angles with the vectors `veca1 , vecb and vecc`, we have,
`d= (mu(veca + vecb + vecc))/3`
(`vecd` passes through the centroid of the triangle with position vectors, `veca , vecb and vecc`)
Again `[veca vecb vecc]vecd = [ vecd vecb vecc] + [vecd vecc vecd] vecb`
`+ [vecd veca vecb]vecc`
From (i) and (ii) , we get `[veca vecb vecc] = [vecd vecc veca] = [ vecd veca vecb] `
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