Motion in two dimensions, in a plane can be studied by expressing position, velocity and acceleration as vector in Cartesian co-ordinates ` vecA=A_(x) hati+A_(y) hatj` where `hati` and `hatj` are unit vectors along x and y directions. respectively and `A_(x)` and `A_(y)` are corresponding components of `vecA` (shown in the figure).Motion can also be studied by expressing vector in circular polar co-ordinates as `vecA=A_(r) hatr+A_(theta) hattheta` where `hatr = vecr/r =costheta hati+sintheta hatj` and `hattheta=-sintheta hati+costheta hatj` are unit vectors along dirction in which 'r' and `'theta'` are increasing.
Express `hati` and `hatj` in terms of `hatr` and `hattheta`.

Motion in two dimensions, in a plane can be studied by expressing position, velocity and acceleration as vector in Cartesian co-ordinates vecA=A_(x) hati+A_(y) hatj where hati and hatj are unit vectors along x and y directions. respectively and A_(x) and A_(y) are corresponding components of vecA (shown in the figure).Motion can also be studied by expressing vector in circular polar co-ordinates as vecA=A_(r) hatr+A_(theta) hattheta where hatr = vecr/r =costheta hati+sintheta hatj and hattheta=-sintheta hati+costheta hatj are unit vectors along dirction in which 'r' and 'theta' are increasing. Show that d/dt (hatr)=omega hattheta where omega=(d theta)/(dt) and d/dt (hattheta)=-omegahatr .

vecA = -2hati + 3hatj - 4hatk and vecB = 3hati - 4hatj + 5hatk where, hati, hatj and hatk are unti vectors along x,y and axes respectively. Find vecA + vecB , vecA - vecB, vecA.vecB and vecA xx vecB .

If veca=2hati+hatj+2hatk and vecb=2hati+hatj+hatk then the unit vector in the direction of veca-vecb is:

If veca=2hati+2hatj+hatk and vecb=2hati+hatj+hatk then the unit vector in the direction of veca-vecb is:

If veca=2hati+hatj+3hatk and vecb=2hati+hatj+2hatk then the unit vector in the direction of veca-vecb is :

If veca=2hati+2hatj+2hatk and vecb=hati+2hatj+2hatk then the unit vector in the direction of veca-vecb is:

If veca=2hati+2hatj+2hatk and vecb=2hati+hatj+2hatk then the unit vector in the direction of veca-vecb is:

Find the unit vector in the direction of the vector : veca =2hati-3hatj+6hatk .

For given vectors, veca=2hati-hatj+2hatk and vecb=-hati+hatj-hatk , find the unit vector in the direction of the vector veca + vecb

If veca=3hati-hatj+2hatk and vecb=-hati-2hatj+4hatk , find a unit vector along the vector (veca+vecb) .