For any vector `vecr`,
` ( vecr.hati) hati + ( vecr.hatj) hatj + ( vecr.hatk) hatk` =

For any vector vecr prove that vecr=(vecr.hati)hati+(vecr.hatj)hatj+(vecr.hatk)hatk .

Statement 1: If veca, vecb are non zero and non collinear vectors, then vecaxxvecb=[(veca, vecb, hati)]hati+[(veca, vecb, hatj)]hatj+[(veca, vecb, hatk)]hatk Statement 2: For any vector vecr vecr=(vecr.hati)hati+(vecr.hatj)hatj+(vecr.hatk)hatk

Statement 1: If veca, vecb are non zero and non collinear vectors, then vecaxxvecb=[(veca, vecb, hati)]hati+[(veca, vecb, hatj)]hatj+[(veca, vecb, hatk)]hatk Statement 2: For any vector vecr vecr=(vecr.hati)hati+(vecr.hatj)hatj+(vecr.hatk)hatk

For any vector vecr, (vecr.hati) ^(2) + (vecr.hatj)^(2) + ( vecr.hatk)^(2) is equal to

For any vector vecr, (vecr.hati) ^(2) + (vecr.hatj)^(2) + ( vecr.hatk)^(2) is equal to

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

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

For any vector vecr = xhati+yhatj+zhatk , prove that vecr = (vecr.hati)hati+(vecr.hatj)hatj+(vecr.hatk)hatk .

Let veca = hati + hatj + hatk and let vecr be a variable vector such that vecr.hati, vecr.hatj and vecr.hatk are posititve integers. If vecr.veca le 12 , then the total number of such vectors is: