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An electric field is given by E=(y hat(i...

An electric field is given by `E=(y hat(i)+ xhat(k))N//C`. Work done in moving a 1C charge from `r_(A)=(2hat(i)+2hat(j))m` to `r_(B)=(4hat(i)+hat(j))m` is

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`W=q int_(r_A)^(r_B) vec E. vec dr`
`=1 times int_(0.2)^(4.1) (E_x dx +E_y dy),=1 times int_(2.2)^(4.1) (ydx+xdy)= int_(2.2)^(4.1) d(xy),[xy]_(2.2)^(4.1)=4 times 1-2 times 2=0`
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An electric field is given by vec(E)=(yhat(i)+xhat(j))N/C . Find the work done (in J) in moving a 1 C charge from vec(r)_(A)=(2hat(i)+2hat(j)) m to vec(r)_(B)=(4hat(i)+hat(j))m .

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The position vectors of three particles of mass m_(1) = 1kg, m_(2) = 2kg and m_(3) = 3kg are r_(1) = ((hat(i) + 4hat(j) +hat(k)) m, r_(2) = ((hat(i)+(hat(j)+hat(k)) m and r_(3) = (2hat(i) - (hat(j) -(hat(2k)) m, respectively. Find the position vector of their center of mass.

The angle between the lines overset(to)( r)=(4 hat(i) - hat(j) )+ lambda(2 hat(i) + hat(j) - 3hat(k) ) and overset(to) (r )=( hat(i) -hat(j) + 2 hat(k) ) + mu (hat(i) - 3 hat(j) - 2 hat(k) ) is

If angle bisector of overline(a) = 2hat(i) + 3 hat(j) + 4 hat(k) and overline(b) = 4hat(i) - 2 hat(j) + 3 hat(k) is overline(c ) = alpha hat(i) + 2 hat(j) + beta hat(k) then

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Find the projection of vec(b)+ vec(c ) on vec(a) where vec(a)= 2 hat(i) -2hat(j) + hat(k), vec(b)= hat(i) + 2hat(j)- 2hat(k), vec(c ) = 2hat(i) - hat(j) + 4hat(k)

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