Related InterviewSolutions

• If a, b,c are the pth, qth, and rth terms of a HP, then the vectors ` vecu= a^(-1) hati +b^(-1) hatj +c^(-1) hatk and vecv = ( q -r) hati + ( q -r) hati + ( r-p) hatj + ( p-q) hatk`A. are parallelB. are othogonalC. satisfy `vecu .vecv =1`D. satisfy `|vecu xx vecv| =hati +hatj +hatk`
• The number of vectors of unit length perpendicular to the vectors ` hata = hati +hatj and vecb = hatj + hatk` isA. 1B. 2C. 4D. infinite
• For any vector `vecr, (vecr.hati) ^(2) + (vecr.hatj)^(2) + ( vecr.hatk)^(2) ` is equal toA. 1B. `|vecr|`C. `vecr`D. `|vecr|^(2)`
• A vector of magnitude 4 which is equally inclined to the vectors `hati +hatj,hatj +hatk and hatk +hati`, isA. `4/sqrt3 (hati -hatj -hatk)`B. ` 4/sqrt3 (hati +hatj -hatk)`C. ` 4/sqrt3 (hati +hatj +hatk)`D. `4/sqrt3 (hati +hatj -hatk)`
• Let ` vecu = u_(1)hati + u_(2)hatj +u_(3)hatk` be a unit vector in ` R^(3) and vecw = 1/sqrt6 ( hati + hatj + 2hatk)` , Given that there exists a vector `vecv " in " R^(3)` such that ` | vecu xx vecv| =1 and vecw . ( vecu xx vecv) =1` which of the following statements is correct ?A. There is exactly one choice for such ` vecv`B. There are exactly two for such `vecv`C. There are exactly for such `vecv`D. There are infinitely many choices for such `vecv`
• IF the force represented by ` 3hati +2hatk` is acting through the point ` 5hati +4hatj -3hatk` , then its moment about th point (1,3,1) isA. ` 14 hati -8 hatj +12hatk`B. ` -14hati +8hatj -12hatk`C. ` -6hati -hatj +9hatk`D. ` 6hati +hatj -9hatk`
• Forces of magnitudes 5 and 3 units acting in the directions ` 6hati + 2hatj + 3hatk and 3 hati - hati +6hatk` respectively act on a particle which is displaced from the point ( 2,2,-1) to ( 4,3,1) . The work done by the forces, isA. 148 unitB. ` 148/7` unitC. 296 unitsD. none of these
• Unit vectors equally inclined to the vectors ` hati , 1/3 ( -2hati +hatj +2hatk) = +- 4/sqrt3 ( 4hatj +3hatk)` areA. `+- 1/sqrt51 (hati - 5hatj +5hatk)`B. ` +- 1/sqrt51 (hati -5hatj -5hatk)`C. `+- 1/sqrtt51 (hati+ 5hatj + 5hatk)`D. none of these
• A force of 39 kg. wt is acting at a point p ( -4,2,5) in the direaction ` 12hati -4hatj -3hatk` . The moment of this force about a line through the origin having the direction of ` 2hati -2hatj + hatk` isA. 76 unitsB. - 76 unitsC. ` 42hati + 144 hatj -24 hatk`D. none of these
• If ` veca, vecb` are unit vectors such that ` |veca +vecb|=1 and |veca -vecb|=sqrt3`, " then " |3veca +2vecb|=`A. 7B. 4C. ` sqrt7`D. `sqrt19`