Find the angle between the vectors:
`vec v underset 1= (3,5,4)` and `vec v underset 2= (2,-2,1)`.

Find the angle between the vectors: vec v underset 1= hat i-2 hat j- 2 hat k and vec v underset 2=2 hat i+ 3 hat j- 6 hat k .

Find the cosine and the sine of the angle between the vectors vec underset(1)(v)= 2 hat i+hat j+3 hat k and vec underset(2)(v)=4 hat i-2 hat j+2 hat k .

Find vec v underset 1 * vec v underset 2 when vec v underset 1= (1,3,5), vec v underset 2= (5,-7,9) .

Find vec v underset 1 . vec v underset 2 when vec v underset 1 = (2,3,-1) , vec v underset 2 = (-1,2,3) .

Find the angle between the vectors vec a and vec b with magnitudes 1 and 1 respectively and when vec a.vec b =1.

Find the sine of the angle between the vectors vec a =3 hat i+hat j+2 hat k and vec b =2hat i-2 hat j+4 hat k .

If the two adjacent sides of two rectangles are represented by vectors vec p=5 vec a-3 vec b ; vec q=- vec a-2 vec b \ and \ vec r=-4 vec a- vec b ; vec s=- vec a+ vec b , respectively, then the angel between the vector vec x=1/3( vec p+ vec r+ vec s) \ and \ vec y=1/5( vec r+ vec s) is

In each of the following problems, components of vec AB along X-axis and Y-axis are respectively a underset 1 and a underset 2 . Find the point B when: a underset 1 = 2, a underset 2 = 3, A(2,-3) .