Find a unit vector parallel to the vector `3 hat i +7 hat j + 4 hat k`.

Find a unit vector parallel to the vector hat i+sqrt(3)hat j

Find a unit vector perpendicular to the vectors hat(j) + 2 hat(k) & hat(i) + hat(j)

Find a unit vector perpendicular to both the vectors 4hat i-hat j+3hat k and -2hat i+hat j-2hat k

Find a unit vector perpendicular to both the vectors hat i-2hat j+3hat k and hat i+2hat j-hat k

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 .

Let ABCD be the parallelogram whose sides AB and AD are represented by the vectors 2 hat i +4 hat j-5 hat k and hat i+2 hat j+3 hat k.Then if vec a is a unit vector parallel to AC then = (a) 1/3(3 hat i-6 hat j-2 hat k) (b) 1/3(3 hat i +6 hat j+2 hat k) (c) 1/7(3 hat i +6 hat j+2 hat k) (d) 1/7(3 hat i +6 hat j-2 hat k)

Dine the unit vector peroendicular to each of the vectors 3 hat i+ hat j 2 hat k and 2 hat i- 2 hat j = 4 hat k .

If vec(a)=4hat(i)-hat(j)+hat(k) and vec(b)=2hat(i)-2hat(j)+hat(k) , then find a unit vector parallel to the vector vec(a)+vec(b) .

The scalar product of the vector hat i+ hat j+ hat k with a unit vector along the sum of vector 2 hat i+4 hat j-5 hat k and lambda hat i+2 hat j+3 hat k is equal to one. Find the value of lambda .

Find the value of a for which the vector 3 hat i + 3 hat j + 9 hat k and hat i + a hat j + 3 hat k are parallel.