InterviewSolution
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InterviewSolution
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Let `veca, vecb, and vecc` be three non- coplanar vectors and `vecd` be a non -zero , which is perpendicular to `(veca + vecb + vecc). Now vecd = (veca xx vecb) sin x + (vecb xx vecc) cos y + 2 (vecc xx veca) `. ThenA. `(vecd. (veca + vecc))/([veca vecb vecc])=2`B. `(vecd. (veca + vecc))/([veca vecb vecc])=-2`C. minimum value of `x^(2) + y^(2) is pi^(2)//4`D. minimum value of `x^(2) + y^(2) is 5 pi^(2)//4` |
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Answer» Correct Answer - b,d `vecd. veca = [veca vecb vecc] cos y=-vecd. (vecb+vecc)` ` or cos y = (vecd. (vecb +vecc))/([veca.vecb.vecc]) ` similarly, ` sin x = (vecd.(veca+vecb))/([veca vecb vecc]) and (vecd.(veca+vecc))/([veca vecb vecc])=-2` `sin x + cos y + 2 = 0` ` or sin x + cos y =-2 ` ` or sin x =-1 , cos y = -1 ` since we want the minimum value of `x^(2) + y^(2) x = -pi//2 , y = pi` ,Therefore, the minimum value of `x^(2) + y^(2) is 5 pi^(2)//4` |
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