Related InterviewSolutions

• Vectors `vecx,vecy,vecz` each of magnitude `sqrt(2)` make angles of `60^0` with each other. If `vecxxx(vecyxx(veczxxvecx)=vecb nd vecxxxvecy=vecc, find vecx, vecy, vecz` in terms of `veca,vecb and vecc`.A. `1/2[(veca-vecb)xx vecc+ (veca + vecb)]`B. `1/2[(veca+vecb)xx vecc+ (veca - vecb)]`C. `1/2[-(veca+vecb)xx vecc+ (veca + vecb)]`D. `1/2[(veca+vecb)xx vecc- (veca + vecb)]`
• If `veca=xhati + y hatj + zhatk, vecb= yhati + zhatj + xhatk and vecc= zhati + xhatj+ yhatk ,, " then " vecaxx (vecbxx vecc) `isA. parallel to ` ( y- z) hati + (z - x) hatj + (x -y) hatk`B. orthogonal to `hati + hatj + hatk`C. orthogonal to ` ( y+z) hati + ( z + x) hatj + ( x + y) hatk`D. orthogonal to `xhati + yhatj + zhatk`
• Let `veca=alphahati+2hatj- 3hatk, vecb=hati+ 2alphahatj - 2hatk and vecc = 2hati - alphahatj + hatk`. Find the value of `6 alpha`. Such that `{(vecaxxvecb)xx(vecbxx vecc)}xx(veccxxveca)=0`
• If `veca,vecb,vecc and vecd` are unit vectors such that `(vecaxxvecb).(veccxxvecd)=1 and veca.vecc=1/2` then (A) `veca,vecb,vecc` are non coplanar (B) `vecb,vecc, vecd` are non coplanar (C) `vecb, vecd` are non paralel (D) `veca, vecd` are paralel and `vecb, vecc` are parallelA. `veca, vecb and vecc` are non- coplanarB. `vecb, vecc and vecd` are non-coplanarC. `vecb and vecd` are non- parallelD. `veca and vecd` are parallel and `vecb and vecc` are parallel
• Let `veca=hati + hatj +hatk,vecb=hati- hatj + hatk and vecc= hati-hatj - hatk` be three vectors. A vectors `vecv` in the plane of `veca and vecb` , whose projection on `vecc is 1/sqrt3` is given byA. `hati-3hatj + 3hatk`B. `-3hati-3hatj +hatk `C. `3hati -hatj + 3hatk`D. `hati+ 3hatj -3hatk`
• Statement 1: Vector `vecc = -5hati + 7 hatj + 2hatk ` is along the bisector of angle between `veca = hati + 2hatj + 2hatk and vecb = 8 hati + hatj - 4hatk`. Statement 2 : `vecc` is equally inclined to `veca and vecb`.A. Both the statements are true and statement 2 is the correct explanation for statement 1.B. Both statements are true but statement 2 is not the correct explanation for statement 1.C. Statement 1 is true and Statement 2 is falseD. Statement 1 is false and Statement 2 is true.
• Which of the following expressionsare meaningful?` vec udot( vec vxx vec w)`b. `( vec udot vec v)dot vec w`c. `( vec udot vec v)dot vec w`d. ` vec uxx( vec vdot vec w)`A. `vecu.(vecvxx vecw)`B. `(vecu.vecv).vecw`C. `(vecu.vecv)vecw`D. `vecu xx (vecv . Vecw)`
• Let `veca=a_(1)hati+a_(2)hatj+a_(3)hatk, vecb=b_(1)hati+b_(2)hatj+b_(3)hatk` and `vecc=c_(1)hati+c_(2)hatj+c_(3)hatk` be three non zero vectors such that `vecc` is a unit vector perpendicular to both `veca` and `vecb` . If the angle between `veca` and `vecb` is `(pi)/6`, then `|(a_(1),a_(2),a_(3)),(b_(1),b_(2),b_(3)),(c_(1),c_(2),c_(3))|^(2)` is equal to
• Let `veca=hati + 2hatj +hatk, vecb=hati - hatj +hatk and vecc= hati+hatj-hatk` A vector in the plane of `veca and vecb` whose projections on `vecc`` `is` `1//sqrt3` isA. `4 hati - hatj + 4hatk`B. `3hati+hatj - 3hatk`C. `2hati+hat- 2hatk`D. `4hati + hatj -4hatk`
• For three vectors `vecu,vecv,vecw` which of the following expressions is not eqal to any of the remaining three?A. `vecu.(vecvxx vecw)`B. `(vecvxx vecw).vecu`C. `vecv.(vecuxx vecw)`D. `(vecuxx vecv).vecw`