`vecA= hati` & `vecB= hatj+hatk`, then find out `vecA.vecB`?

If veca=hati+hatj + hatk and vecb = hati - 2 hatj+hatk then find the vector vecc such that veca.vecc =2 and veca xx vecc=vecb .

vectors veca,vecb and vecc are of the same length and when taken pair-wise they form equal angles. If veca=hati+hatj and vecb=hatj+hatk then find vector vecc .

If veca = hati + hatj + hatk , vecb = hatj - hatk then find a vector vecc , such that veca xx vecc = vecb and veca .vecc = 3 .

If veca=hati+hatj+hatk,hatb=hati-hatj+hatk,vecc=hati+2hatj-hatk , then find the value of |{:(veca.veca,veca.vecb,veca.vecc),(vecb.veca,vecb.vecb,vecb.vecc),(vecc.veca,vecc.vecb,vecc.vecc):}|

If veca=-hati+hatj+hatk andvecb=2hati+0hatj+hatk then find vector vecc satisfying the following conditions, (i) that it is coplaner with veca and vecb , (ii) that it is bot "to" vecb and (iii) that veca.vecc=7 .

If veca and vecb are vectors in space given by veca= (hati-2hatj)/sqrt5and vecb= (2hati + hatj + 3hatk)/sqrt14 then find the value of (2veca + vecb) . [(vecaxxvecb) xx (veca- 2vecb)]

If vec a= 3hati+hatj+9 hat k and vecb = hati +lambda hat j+3 hat k then find the value of lambda for which the vector (veca+vecb) and (veca-vecb) are perpendicular to each other.

If veca.veci=veca.(hati+hatj)=veca.(hati+hatj+hatk) . Then find the unit vector veca .

If veca=2hati + 3hatj+ 8hatk is perpendicular to vecb= 4hati-4hatj + alphahatk , then find the value of alpha