What is the projection of `vec(a)=(2hat(i)-hat(j)+hat(k)) ` on `vec(b)=(hat(i)-2hat(j)+hat(k))?`

The projection of vec(a)=2hat(i)-hat(j)+hat(k) on vec(b)=hat(i)-2hat(j)+hat(k) is equal to :

Find the projection of vec(a) = 2 hat(i) - hat(j) + hat(k) on vec(b) = hat(i) - 2 hat(j) + hat(k) .

Find the area of the parallelogram whose adjacent sides are represented by the vectors (i) vec(a)=hat(i) + 2 hat(j)+ 3 hat(k) and vec(b)=-3 hat(i)- 2 hat(j) + hat(k) (ii) vec(a)=(3 hat(i)+hat(j) + 4 hat(k)) and vec(b)= ( hat(i)- hat(j) + hat(k)) (iii) vec(a) = 2 hat(i)+ hat(j) +3 hat(k) and vec(b)= hat(i)-hat(j) (iv) vec(b)= 2 hat(i) and vec(b) = 3 hat(j).

Find the angle between the vectors vec(a) and vec(b) , when (i) vec(a)=hat(i)-2hat(j)+3 hat(k) and vec(b)=3hat(i)-2hat(j)+hat(k) (ii) vec(a)=3 hat(i)+hat(j)+2hat(k) and vec(b)=2hat(i)-2hat(j)+4 hat(k) (iii) vec(a)=hat(i)-hat(j) and vec(b)=hat(j)+hat(k) .

Find ( vec (a) xxvec (b)) and |vec(a) xx vec (b)| ,when (i) vec(a) = hat(i)-hat(j)+ 2hat(k) and vec(b)= 2 hat(i)+3 hat(j)-4hat(k) (ii) vec(a)= 2hat (i)+hat(j)+ 3hat(k) and vec(b)= 3hat(i)+5 hat(j) - 2 hat(k) (iii) vec(a)=hat(i)- 7 hat(j)+ 7hat(k) and vec(b) = 3 hat(i)-2hat(j)+2 hat(k) (iv) vec(a)= 4hat(i)+ hat(j)- 2hat(k) and vec(b) = 3 hat(i)+hat(k) (v) vec(a) = 3 hat(i) + 4 hat(j) and vec(b) = hat(i)+hat(j)+hat(k)

Find the value of lambda for which the vectors vec(a), vec(b), vec(c) are coplanar, where (i) vec(a)=(2hat(i)-hat(j)+hat(k)), vec(b) = (hat(i)+2hat(j)+3hat(k) ) and vec(c)=(3 hat(i)+lambda hat(j) + 5 hat (k)) (ii) vec(a)lambda hat(i)-10 hat(j)-5k^(2), vec(b) =-7hat(i)-5hat(j) and vec(c)= hat(i)--4hat(j)-3hat(k) (iii) vec(a)=hat(i)-hat(j)+hat(k), vec(b)= 2hat( i) + hat(j)-hat(k) and vec(c)= lambda hat(i) - hat(j) + lambda hat(k)

Find the scalar projection of vec(b) on vec(a) , when : vec(a)=2hat(i)+2hat(j)-hat(k) and vec(b)=2hat(i)-hat(j)-4hat(k)

Find the scalar projection of vec(b) on vec(a) , when : vec(a)=2hat(i)+hat(j)+2hat(k) and vec(b)=hat(i)+2hat(j)+hat(k) .