If `veca,vecb and vecc` are three mutually perpendicular unit vectors and `vecd` is a unit vector which makes equal angal with `veca,vecb and vecc`, then find the value of `|veca+vecb+vecc+vecd|^(2)`.

If `veca,vecb and vecc` are three mutually perpendicular unit vectors

1.	If `veca,vecb and vecc` are three mutually perpendicular unit vectors and `vecd` is a unit vector which makes equal angal with `veca,vecb and vecc`, then find the value of `\|veca+vecb+vecc+vecd\|^(2)`.
Answer» `\|veca+vecb+vecc+vecd\|^(2)=sum\|veca\|^(2)+2sumveca.vecb=4+2vecd.(veca+vecb+vecc) " " (veca,vecb,vecc "are mutually perpendicular")` `Let vecd=lambdaveca+muvecb+v vecc. Then vecd.veca=vecd.vecb=vecd.vecc=costheta`Therefore, `lambda=mu=v=costheta` ` lambda^(2)+mu^(2)+v^(2)=1Rightarrow3cos^(2)theta=1costheta=1/sqrt3` `\|veca+vecb+vecc+vecd\|^(2)=4+-(2.3)/sqrt3=4+-2sqrt3`

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If `veca,vecb and vecc` are three mutually perpendicular unit vectors and `vecd` is a unit vector which makes equal angal with `veca,vecb and vecc`, then find the value of `|veca+vecb+vecc+vecd|^(2)`.

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