Can you have `vecAxxvecB=vecA.vecB` with A!=0 and B!=0?` What if one of the two vectors is zero?

Assertion : The direction of a zero (null) vector is indeteminate. Reason : We can have vecAxx vecB = vecA *vecB with vecA ne vec0 and vecB ne vec0 .

If for two vector vecA and vecB , vecAxxvecB=0 then

What is the value of (vecA+vecB),(vecAxxvecB) ?

If vecAxxvecB=vecC , then choose the incorrect option : [ vecA and vecB are non zero vectors]

If two out to the three vectors , veca, vecb , vecc are unit vectors such that veca + vecb + vecc =0 and 2(veca.vecb + vecb .vecc + vecc.veca) +3=0 then the length of the third vector is

If veca and vecb are two vectors such that |veca xx vecb|= veca.vecb , then what is the angle between veca and vecb ?

Let veca,vecb and vecc be non-zero vectors such that no two are collinear and (vecaxxvecb)xxvecc=1/3|vecb||vecc|veca If theta is the acute angle between the vectors vecb and vecc then sin theta equals

Let veca, vecb and vecc be non-zero vectors such that no two are collinear and (vecaxxvecb)xxvecc=1/3 |vecb||vecc|veca if theta is the acute angle between vectors vecb and vecc then find value of sin theta .

Solve vecrxxvecb=vecaxxvecb, where veca, vecb are two given vectors