InterviewSolution
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InterviewSolution
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Lelt two non collinear unit vectors `hata and hatb` form and acute angle. A point P moves so that at any time t the position vector `vec(OP)` (where O is the origin) is given by `hatacost+hatbsint.` When P is farthest from origin O, let M be the length of `vec(OP) and hatu` be the unit vector along `vec(OP)` Then (A) `hatu= (hata+hatb)/(|hata+hatb|) and M=(1+hata.hatb)^(1/2)` (B) `hatu= (hata-hatb)/(|hata-hatb|) and M=(1+hata.hatb)^(1/2)` (C) `hatu= (hata+hatb)/(|hata+hatb|) and M=(1+2hata.hatb)^(1/2)` (D) `hatu= (hata-hatb)/(|hata-hatb|) and M=(1+2hata.hatb)^(1/2)`A. `,hatu = (hata+hatb)/(|hata + hatb|) and M = (1 + hata.hatb)^(1//2)`B. `,hatu = (hata-hatb)/(|hata - hatb|) and M = (1 + hata.hatb)^(1//2)`C. `hatu = (hata+hatb)/(|hata + hatb|) and M = (1 + 2hata.hatb)^(1//2)`D. `,hatu = (hata-hatb)/(|hata - hatb|) and M = (1 + 2hata.hatb)^(1//2)` |
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Answer» Correct Answer - a `|vec(OP)|= |hata cos t +hatb sin t |` `= (cos^(2)t + sin^(2) t + 2cos t tin t hata.hatb) ^(1//2)` ` (1 + 2 cos t tin t hata.hatb)^(1//2)` ` (1+sin 2t hata.hatb)^(1//2)` `|vec(OP)|_(max)= (1+hata.hatb)^(1//2)"when " t=pi//4` `hatu = (hata+hatb)/(sqrt2(|hata+hatb|)/sqrt2)= (hata+hatb)/(|hata+hatb|)` |
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