If `vec(r)=[ucos theta(hat(i))+u sin theta(hat(j))]t+(1)/(2)g(-hat(j))t^(2)` then calculate equation of trajectory.

If vec(A) = (1)/(sqrt2) cos theta hat(i) + (1)/(sqrt2) sin theta hat(j) , what will be the unit vector perpendicular to vec(A)

If Vectors vec(A)= cos omega t(i)+ sin omega t(j) and vec(B)=cosomegat/(2)hat(i)+sinomegat/(2)hat(j) are functions of time. Then the value of t at which they are orthogonal to each other is

If vec(a)=2hat(i)+2 hat(j)+3hat(k), vec(b)=-hat(i)+2hat(j)+hat(k) and vec(c)=3hat(i)+hat(j) are three vectors such that vec(a)+t vec(b) is perpendicular to vec(c) , then what is t equal to ?

Find the net torque of these following forces about origin vec(F)_(1) = hat(i) - hat(j) acting at vec(r_(1))= 2hat(i) + hat(j), vec(F)_(2) = -hat(i) + hat(j) acting at vec(r_(2)) =hat(i) +2hat(j) & vec(F)_(3) = hat(i) +hat(j) acting at vec(r )_(3) = hat(i) - hat(j) .

If Vectors vec(A)= cos omega t hat(i)+ sin omega t hat(j) and vec(B)=(cos)(omegat)/(2)hat(i)+(sin)(omegat)/(2)hat(j) are functions of time. Then the value of t at which they are orthogonal to each other is

Prove that if vec(u)=u_(1)hat(1)hat(i)+u_(2)hat(j) and vec(v)=v_(1)hat(i)+v_(2)hat(j) are non - zero vectors, then they are parallel if and only if u_(1)v_(2)-u_(2)v_(1)=0 .