If `overset(vec)(F)` is force vector, `overset(vec)(v)` is velocity , `overset(vec)(a)` is acceleration vector and `overset(vec)(r)` vector is displacement vector `w.r.t.` mean position than which of the following quantities are always non-negative in a simple harmonic motion along a straight line ?

If theta is smaller angle between force vector vec(F) and velocity vector vec(v) then Fv cos theta represents

The angle between two vectors vec(A) and vec(B) is theta . The resultant of these vectors vec(R ) makes an angle of theta//2 with A. which of the following is true?

The vector relation between linear velocity vec v ,angular velocity vec omega and radius vector vec r is given by

If a,b,c are non coplanar vectors prove that the points having the following position vectors are collinear: vec a,vec b,3vec a-2vec b

For non- zero vectors overset(to)(a) , overset(to)(b), overset(to)(c ),|(vec(a)xx vec(b)). vec(c )| =|vec(a)||vec(b)||vec(c )| holds if and only if

A moving perticle of mass m is acted upon by five forces overset(vec)(F_(1)),overset(vec)(F_(2)),overset(vec)(F_(3)),overset(vec)(F_(4)) and overset(vec)(F_(5)) . Forces overset(vec)(F_(2)) and overset(vec)(F_(3)) are conservative and their potential energy funcations are U and W respectively. Speed of the particle changes from V_(a) to V_(b) when it moves from position a to b . Choose the correct option :

A moving perticle of mass m is acted upon by five forces overset(vec)(F_(1)),overset(vec)(F_(2)),overset(vec)(F_(3)),overset(vec)(F_(4)) and overset(vec)(F_(5)) . Forces overset(vec)(F_(2)) and overset(vec)(F_(3)) are conservative and their potential energy funcations are U and W respectively. Speed of the particle changes from V_(a) to V_(b) when it moves from position a to b . Choose the correct option :

If vec(a),vec(b),vec (c ) are non - coplanar vectors vec (r) . vec(a) = vecr . vec(b) = vecr.vec(c ) = 0 , show that vec (r ) is a zero vector .

Which of the following quantities are always zero in a S.H.M. ? Here, vec(r),vec(upsilon) and vec(a) represent amplitude, velocity and acceleration vectore.