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Calculate the are of the triangle determined by the two vectors `vec(A)=3hat(i)+4hat(j)` and `vec(B)=-3hat(i)+7hat(j).` |
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Answer» We know thet the half of magnitude of the cross product of two vectors gives the area of the triangle. `vec(A)xxvec(B)=|(hat(i), hat(j), hat(k)) ,(3,4,0), (-3 ,7 ,0)|` `=hat(i)(0-0)-hat(j)(0-0)+hat(k)(21+12)=33hat(k)` Taking magnitude `|vec(A)xxvec(B)|=sqrt(33^(2))=33`. So area of triangle `=1/2|vec(A)xxvec(B)|=33/2sq.`unit. |
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