Find the scalar and vector projections of ` 3 hat (i) - hat (j) + 4 hat (k) ` on ` 2 hat (i) + 3 hat (j) - 6 hat (k) `

The scalar projection of vec(a) = 2 hat (i) - 3hat(j) + hat (k) on vec (b) = 3 hat(i) - 6 hat (j) - 2 hat (k)

find the projection of 3hat i - hat j + 4hat k on 2 hat i + 3 hat j -6 hat k

Find the scalar and vector projection of vec(b) on a vec (a) where vec(a) = hat (i) + 2 hat (j) + 2 hat (k) and vec (b) = hat (j) + 2 hat (k)

Find lambda where projection of vec (a) = lambda hat (i) + hat (j) + 4 hat (k) on vec (b) = 2 hat (i) + 6 hat (i) + 3 hat (k) is 4 unit

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)

The scaler product of the vector hat (i) + hat (j) + hat (k) with the unit vector along the sum of vectors 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 area of the parallelogram whose Whose diagonals are the vectors 3 hat (i) + hat (j) - 2 hat (k) and hat (i) - 3 hat (j) + 4 hat (k)

In each of the following show that the given vectors are coplanar: 4 hat (i) + 2 hat (j) + hat (k) , 2 hat (i) - hat (j) + 3 hat (k) , 8 hat (i) + 7 hat (k)

Find the area of triangle whose vertices have position vectors hat (i) + hat (j) + 2 hat (k) , 2 hat (i) + 2 hat (j) + 3 hat (k) and 3 hat (i) - hat (j) - hat (k)

Find the vector alpha which is perpendicular to both 4 hat (i) + 5 hat (j) - hat (k) and hat (i) - 4 hat (j) + 5 hat (k) and which satisfies the relation alpha . beta = 21 where beta = 3 hat (i)+ 5 hat (j) - hat (k)