Let `hat u= u_1 hat i+u_2 hat j+u_3 hat k` be a unit vector in be a unit vector in `RR^3 and hat w=1/sqrt6 (hat i+hat j+2 hat k)`.Given that there exists vector `hat v` in `RR^3` such that `|hat u xx vec v|=1 and hat w . (hat u xx vec v)=1`. Which of the following statement(s) is(are) correct?

Let widehat u=u_(1)hat i+u_(2)hat j+u_(3)hat k be a unit vector in be a unit vector in R^(3) and widehat w=(1)/(sqrt(6))(hat i+hat j+2hat k). Given that there exists vector hat v in R^(3) such that |widehat u xxvec v|=1 and widehat w.(widehat u xxvec v)=1. Which of the following statement(s) is(are) correct?

Find a unit vector parallel to the resultant of vectors vec A = 3 hat I + 3 hat j - 2 hat k and vec B= hat i- 5 hat j + hat k .

Find a unit vector in the opposite direction of bar(u) . Where bar(u) = 8 hat(i) + 3 hat(j) - hat(k) .

The unit vector perpendicular to vec A = 2 hat i + 3 hat j + hat k and vec B = hat i - hat j + hat k is

If vec a*hat i=vec a*(hat i+hat j)=vec a*(hat i+hat j+hat k) then find the unit vector vec a

Figure 2 (EP). 13 shows the orientatione of two vectors vec u and vec v in the (XY) plane. If vec u = a hat I + b hat j and vec v = p hat + q hat j which of the following is correct ? .

Let hat u= hat i+ hat j , hat v= hat i- hat ja n d hat w= hat i+2 hat j+3 hat kdot If hat n is a unit vector such that hat udot hat n=0a n d hat vdot hat n=0, then find the value of | hat wdot hat n|dot

vec u=hat i+hat j,vec v=hat i-hat j and vec w=hat i+2hat j+3hat k .If widehat n is a unit vector such that vec u*widehat n=0 and vec v*widehat n then |vec w*widehat n| is equal to

If vec A = hat i + 3 hat j + 2 hat K and vec B = 3 hat i + hat j + 2 hat k , then find the vector product vec A xx vec B .

If vec a=3hat i-2hat j+hat k and vec b=-hat i+hat j+hat k then the unit vector parallel to vec a+vec b, is