A loop of wire is placed in a magnetic field `vec(B)=0.02 hat(i) T`. Then the flux through the loop if its area vector
`vec(A)=30hat(i)+16hat(j)+23hat(k) cm^(2)` is

Find the angle between the vectors : vec(a)=hat(i)+hat(j)-hat(k) " and " vec(b)=hat(i)-hat(j)+hat(k)

Find the angle between the vectors vec(a) = hat(i) + hat(j) + hat(k) and vec(b) = hat(i) - hat(j) + hat(k) .

Vector vec(A)=hat(i)+hat(j)-2hat(k) and vec(B)=3hat(i)+3hat(j)-6hat(k) are :

Vector vec(A)=hat(i)+hat(j)-2hat(k) and vec(B)=3hat(i)+3hat(j)-6hat(k) are :

The unit vector normal to the plane containing vec(a)=(hat(i)-hat(j)-hat(k)) and vec(b)=(hat(i)+hat(j)+hat(k)) is

Find the area of the parallelogram whose adjacent sides are represented by the vectors (i) vec(a)=hat(i) + 2 hat(j)+ 3 hat(k) and vec(b)=-3 hat(i)- 2 hat(j) + hat(k) (ii) vec(a)=(3 hat(i)+hat(j) + 4 hat(k)) and vec(b)= ( hat(i)- hat(j) + hat(k)) (iii) vec(a) = 2 hat(i)+ hat(j) +3 hat(k) and vec(b)= hat(i)-hat(j) (iv) vec(b)= 2 hat(i) and vec(b) = 3 hat(j).

a. Prove that the vector vec(A)=3hat(i)-2hat(j)+hat(k) , vec(B)=hat(i)-3hat(j)+5hat(k), and vec(C )=2hat(i)+hat(j)-4hat(k) from a right -angled triangle. b. Determine the unit vector parallel to the cross product of vector vec(A)=3hat(i)-5hat(j)+10hat(k) & =vec(B)=6hat(i)+5hat(j)+2hat(k).

a. Prove that the vector vec(A)=3hat(i)-2hat(j)+hat(k) , vec(B)=hat(i)-3hat(j)+5hat(k), and vec(C )=2hat(i)+hat(j)-4hat(k) from a right -angled triangle. b. Determine the unit vector parallel to the cross product of vector vec(A)=3hat(i)-5hat(j)+10hat(k) & =vec(B)=6hat(i)+5hat(j)+2hat(k).

The magnetic flux linked with the loop of a wire of area vector (30 hat i + 16 hat j + 23 hat k) cm^(2) is 5 mu Wb. Calculate the magnetic field acting at right angle to the plane of the loop of the wire.