1.

Let veca, vecb and vecc be three mutually perpendicular unit vectors. If vecd is a linear combination of veca, vecb and vecc such that vecd makes equal acute angles with all three vectors veca, vecb and vecc and |vecd|=2, then the value of |veca + vecb, vecc + vecd| is

Answer»

`sqrt(3) +2`
`sqrt(3)-1`
`sqrt(2+sqrt(5))`
`sqrt(7 + 2sqrt(3))`

Solution :SUPPOSE`VECD = x_(1)veca + x_(2) vecb + x_(3) vecc`
where `x_(1), x_(2)` and `x_(3)` are real numbers.
`rArr vecd.veca = x_(1) rArr x_(1) = |vecd| cos THETA`
where `theta`= angle between `vecd` and `veca`
=angle between `vecd` and `vecc`
Similarly `x_(2) = |vecd| cos theta`
`x_(3) = |vecd| cos theta`
`rArr cos^(2)theta = 1/3 rArr cos theta = 1/sqrt(3)`
`|veca + vecb +vecc + vecd|^(2) = 3+4 + 6 cos theta`
`=7 + 6/sqrt(3) = 7+ 2sqrt(3)`


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