Show that power (P)= `vecF*vecV` (Where`vec V`= velocity and `vecF` = force)

Show that P= vecF *vecv where P is the power , vecF is the force and vecv is the velocity.

ABCD is a quadrilateral and E is the point of intersection of the lines joining the middle points of opposite side. Show that the resultant of vec (OA) , vec(OB) , vec(OC) and vec(OD) = 4 vec(OE) , where O is any point.

Show that the vectors 2 vec a- vec b+3 vec c , vec a+ vec b-2 vec ca n d vec a+ vec b-3 vec c are non-coplanar vectors (where vec a , vec b , vec c are non-coplanar vectors)

If vec (a) xx vec(b) = vec (c ) xx vec(d) and vec (a) xx vec ( c) = vec (b) xx vec (d ) , show that vec(a) - vec (d) is parallel vec(b) - vec (c) , where to vec (a) != vec (d) and vec ( b) != vec (c )

If vec p , vec q , vec r denote vector vec bxx vec c , vec cxx vec a , vec axx vec b , respectively, show that vec a is parallel to vec qxx vec r , vec b is parallel vec rxx vec p , vec c is parallel to vec pxx vec q .

If the angular frequency of a particle executing SHM is omega and its maximum velocity is v_(m) , then show that the relation between its velocity v and acceleration a is a=-omegasqrt(v_(m)^(2)-v^(2)) .

Let vec a, vec b, and vec c be three non coplanar unit vectors such that the angle between every pair of them is pi/3 . If vec a xx vec b+ vecb xx vec c=p vec a + q vec b + r vec c where p,q,r are scalars then the value of (p^2+2q^2+r^2)/(q^2) is

If |veca+vecb|= |veca-vecb| ,(where veca and vec b are any vector) then show that veca and vecb are perpendicular to each other.

If in triangle ABC, vec(AB) = vecu/|vecu|-vecv/|vecv| and vec(AC) = (2vecu)/|vecu| , " where " |vecu| ne |vecv| , then (a)1 + cos 2A + cos 2B + cos 2C=0 (b) sin A = cos C (c)projection of AC on BC is equal to BC (d) projection of AB on BC is equal to AB

Show that for ideal gas C_(P ) - C_(v ) = R and gamma =1 +(2)/(f ) , where f is the degrees of freedom of the molecule .