InterviewSolution
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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 |
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Answer» `sqrt(3) +2` 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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