Show that `vec a=(hati-hat j)/(sqrt(2))` is a unit vector.

vec a=hat i+hat j+hat k,vec b=2hat i-hat j+3hat k and vec c=hat i-2hat j+hat k find a unit vector in a direction parallel to vector (2vec a-vec b+3vec c)

If vec a=hat i+hat j and vec b=4hat i-hat j ,find a unit vector in the direction of the vector (2vec a-vec b)

If vec a=hat i+hat j and vec b=4hat i-hat j find a unit vector in the direction of the vector (2vec a-vec b); also find vector and scalar components of (2vec a-vec b) along two coordinate axes.

If a and b are vectors in space given by vec a=(hat i-2hat j)/(sqrt(5)) and vec b=(hat 2i+hat j+3hat k)/(sqrt(14)), then find the value of (2vec a+vec b)*[(vec a xxvec b)xx(vec a-2vec b)]

Find the angles which the vector vec a=hat i-hat j+sqrt(2)hat k makes with the coordinate axes.

Find the angles which the vector vec a=hat i-hat j+sqrt(2)hat k makes with the coordinate axes.

If vec a= hat i+ hat j+ hat k , vec b=2 hat i- hat j+3 hat k a n d vec c= hat i-2 hat j+ hat k find a unit vector parallel to 2 vec a- vec b+3 vec cdot

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

If vec a=hat i+2hat j+hat k,vec b=2hat i+hat j and vec c=3hat i-4hat j-5hat k then find a unit vector perpendicular to both of the vector (vec a-vec b) and (vec c-vec b)

If vec(a)=2hat(i)-hat(j)+2hat(k) and vec(b)=6hat(i)+2hat(j)+3hat(k) , find a unit vector parallel to vec(a)+vec(b) .