If `hat(a) and hat(b)` are the unit vectors along `vec(a) and vec(b)` respectively, then what is the projection of `vec(b) ` on `vec(a)`?

If vec a=hat i-hat j and vec b=-hat j+hat k find the projection of vec a on vec b

If vec(a) = 2 hat(i) + 3hat(j) + 6hat(k) and vec(b) = 3hat(i) + 4hat(j) , then ("projection of " vec(a) " on " vec(b))/("projection of" vec(b) " on " vec(a))

If vec(a) = 2hat(i) + hat(j) - hat(k) and vec(b) = hat(i) - hat(k) , then projection of vec(a) on vec(b) will be :

If vec(a) = 2hat(i) + hat(j) - hat(k) and vec(b) = hat(i) - hat(k) , then projection of vec(a) on vec(b) will be :

(a) Prove that the normal to the plane containing three points whose position vectors are vec(a), vec(b), vec(c ) lie in the direction of vec(b)xx vec(c )+vec(c )xx vec(a)+vec(a)xx vec(b) . (b) Find the unit vector perpendicular to the plane ABC, where the position vectors of A, B and C are : 2hat(i)-hat(j)+hat(k), hat(i)+hat(j)+2hat(k) and 2hat(i)+hat(k) respectively.

vec(A) and vec(B) are two vectors given by vec(A)=2hat(i)+3hat(j) and vec(B)=hat(i)+hat(j). The magnitude of the component of vec(A) along vec(B) is