State the direction of velocity of a particle with position vector given by`bar r = {a cos wt} hati + a sin wt hatj`.

A particle is moving in a circle of radius r with constant angular velocity omega . At any point (r, theta ) on its path , its position vector is vec(r ) = r cos theta hat(i) + r sin theta hat(j) . Show that the velocity of the particle has no component along the radius.

Find the vector equation of a line which passes throught the point with position vector hati - 2hat j+4hatk and is in the direction of hati + 2hatj - hatk . Also reduce it to cartesian form.

Find the distance of the point with position vector 2 hati+ hatj- hatk from the plane vecr .( hati- 2 hatj+ 4 hatk)=9 .

What is time period of a particle moving in the equation sin^2wt .

Find the direction cosines of the vector hati+2hatj+3hatk .

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