If `vecA=2hati-2hatj-hatk` and `vecB=hati+hatj`, then :
(a) Find angle between `vecA` and `vecB`.
(b) Find the projection of resultant vector of `vecA` and `vecB` on x-axis.
(c) Find a vector which is, if added to `vecA, gives a unit vector along y-axis.

Explanation

(a) Let the angle between `vecA` and `vecB` is `theta`, then `cos theta=(vecA.vecB)/(AB)=((2hati-2hatj-hatk).(hati+hatj))/(|2hati+2hatj-hatk|.|hati+hatj|)=(0)/(3sqrt(2))=0rArrtheta=90^(@)`
(b) Resultant `(vecR)=vecA+vecB=(2hati-2hatj-hatk)+(hati+hatj)=3hati-hatj-hatk therefore` projection of resultant on x-axis =3
(c) Required vector `=hatj-vecA=hatj-(2hati-2hatj-hatk)=-2hati+3hatj+hatk`