Find the cosine of the angle between the vectors
` vec ( a ) = 3 hat (i) + 2 hat (k) and vec(b) = 2 hat (i) - 2 hat (j) + 4 hat (k) `

find the angle between the vectors vec a= 3 hat i +2 hat k and vec b = 2 hat i -2 hat j + 4 hat k

Find the scalar product of the following pair of vectors and the angle between them : vec (a) = 2 hat (i) - 5 hat (j) + 3 hat (k) and vec (b) = hat (i) - 2 hat (j) - 4hat (k)

Find the area of triangle (i) drawn on the vectors vec(a) = 6 hat (i) + 2 hat (j) - 3 hat (k) and vec (b) = 4 hat (i) - hat (j) - 2 hat (k)

Find the scalar product of the following pair of vectors and the angle between them : vec(a) = 2 hat (i) + 3 hat (j) - 4 hat (k) and vec(b) = hat (i) + 2 hat (j) + hat (k)

Find the angle between the vectors vec a= hat i+hat j-hat k and vec b=hat i-hat j+hat k

Find the vector of magnitude 3, bisecting the angle between the vectors vec a=2 hat i+ hat j- hat k and vec b= hat i-2 hat j+ hat kdot

Find a unit vector perpendicular to both the vector vec(a) = 2 hat(i) + hat(j) - 2 hat(k) and vec(b) = 3 hat (i) - hat (j) + hat (k)

Find the scalar and vector components of vec(a) in the direction of vec(b) where vec(a) = 3 hat (i) + vec(j) + 3 hat (k) and vec(b) = hat (i) - hat (j) - hat (k)

In each of the following show that the given vectors are coplanar: vec(a) = hat (i) + hat (j) - 6 hat (k) , vec(b) = hat (i) + 3 hat (j) + 4 hat (k) , vec(c) = 2 hat (i) + 5 hat (j) + 3 hat (k)

If vectors vec (a) = p hat (i) + 8 hat (j) + 6 hat (k) and vec (b) = - 3 hat (i) + 4 hat (j) + q hat (k) are parallel , find p and q