Let `vec(a) = hat(i) + hat(j), vec(b) = 3 hat(i) + 4 hat(k) and vec (b) = vec(c) + vec(d)`, where `vec(c)` is parallel to `vec(a) and vec(d) ` is perpendicular to `vec(a)`.
What is `vec(c)` equal to ?

Consider the following for the next two items that follows Let vec(a) = hat(i) + hat(j), vec(b)= 3hat(i) + 4hat(k) and vec(b) =vec(c ) +vec(d) , where vec(c ) is parallel to vec(a) and vec(d) is perpendicular to vec(a) What is vec(c ) equal to ?

If vec(a)=2hat(i)+2 hat(j)+3hat(k), vec(b)=-hat(i)+2hat(j)+hat(k) and vec(c)=3hat(i)+hat(j) are three vectors such that vec(a)+t vec(b) is perpendicular to vec(c) , then what is t equal to ?

If vec(a) = hat(i) + hat(j) + hat(k) and vec(b) = hat(j) - hat(k) , find a vector vec(c ) , such that vec(a) xx vec(c ) = vec(b) and vec(a).vec(c ) = 3 .

If vec(a)= hat(i) + hat(j) + hat(k) and vec(b)= hat(j)-hat(k) , then find vec(c ) such that vec(a ) xx vec(c )= vec(b) and vec(a).vec(c )=3 .

Given vec (a) = 4 hat (i) + 5 hat (j) - hat (k), vec(b) = hat (i) - 4 hat (j) + 5 hat (k) If |vec (c ) | = 21 and vec(c ) is perpendicular to vec(a) and vec (b ) , find in component form the vector vec(c )

If vec a= hat i+ hat j+ hat k , vec c= hat j- hat k , vec adot vec b=3 and vec ax vec b= vec c , then vec b is equal to

If vec a= hat i+ hat j+ hat k , vec c= hat j- hat k , vec adot vec b=5 and vec ax vec b= vec c , then vec b is equal to