Related InterviewSolutions

• The points with position vectors `alpha hati+hatj+hatk, hati-hatj-hatk, hati+2hatj-hatk, hati+hatj+betahatk` are coplanar ifA. `(1-alpha)(1+beta)=0`B. `(1-alpha)(1-beta)=0`C. `(1+alpha)(1+beta)=0`D. `(1+alpha)(1-beta)=0`
• The value of `veca.(vecb+vecc)xx(veca+vecb+vecc)`, isA. `2[veca vecb vecc]`B. `[veca vecb vecc]`C. 0D. None of these
• Let `veca=2hati+3hatj-hatk` and `vecb=hati-2hatj+3hatk`. Then , the value of `lamda` for which the vector `vecc=lamdahati+hatj+(2lamda-1)hatk` is parallel to the plane containing `veca` and `vecb`. IsA. `1`B. `0`C. `-1`D. `2`
• If `veca=hati-2hatj+3hatk, vecb=2hati+3hatj-hatk` and `vecc=rhati+hatj+(2r-1)hatk` are three vectors such that `vecc` is parallel to the plane of `veca` and `vecb` then`r` is equal to,A. `1`B. `0`C. `2`D. `-1`
• Let `vecr, veca, vecb` and `vecc` be four non-zero vectors such that `vecr.veca=0, |vecrxxvecb|=|vecr||vecb|,|vecrxxvecc|=|vecr||vecc|` then `[(veca, vecb, vecc)]=`A. `-1`B. `0`C. `1`D. `2`
• Statement 1: Let `vecr` be any vector in space. Then, `vecr=(vecr.hati)hati+(vecr.hatj)hatj+(vecr.hatk)hatk` Statement 2: If `veca, vecb, vecc` are three non-coplanar vectors and `vecr` is any vector in space then `vecr={([(vecr, vecb, vecc)])/([(veca, vecb, vecc)])}veca+{([(vecr, vecc, veca)])/([(veca, vecb, vecc)])}vecb+{([(vecr, veca, vecb)])/([(veca, vecb, vecc)])}vecc`A. `1`B. `2`C. `3`D. `4`
• A solution of the vector equation `vecrxxvecb=vecaxxvecb`, where `veca, vecb` are two given vectors is where `lamda` is a parameter.A. `vecr=lamdavecb`B. `vecr=veca+lamdavecb`C. `vecr=vecb+lamdaveca`D. `vecr=lamdaveca`
• If `veca, vecb, vecc` are three non-zero non-null vectors are `vecr` is any vector in space then `[(vecb, vecc, vecr)]veca+[(vecc, veca, vecr)]vecb+[(veca, vecb, vecr)]vecc` is equal toA. `2[(veca, vecb, vecc)]vecr`B. `3[(veca, vecb, vecc)]vecr`C. `[(veca, vecb, vecc)]`D. None of these
• Which of the following expressions are meaningful?A. `vecu.(vecvxxvecw)`B. `(vecu.vecv).vecw`C. `(vecu.vecv)vecw`D. `vecuxx(vecv.vecw)`
• The number of distinct values of `lamda`, for which the vectors `-lamda^(2)hati+hatj+hatk, hati-lamda^(2)hatj+hatk` and `hati+hatj-lamda^(2)hatk` are coplanar, is