Question

Find the area of the triangle formed by the tips of the vectors `vec(a) = hati - hatj - 3hatk, vec(b) = 4hati - 3hatj +hatk` and `vec(c) = 3 hati - hatj +2 hatk`.

Answer 1

Let ABC is the triangle formed by the points A,B and C. Then
`bar(AB)=oversetrightarrow(B)-oversetrightarrow(A)=(4hati-3hatj+hatk)-(hati-hatj-3hatk)=3hati-2hatj+4hatk`
`bar(AC)=oversetrightarrow(C)-oversetrightarrow(A)=(3hati-3hatj+2hatk)-(hati-hatj-3hatk)=2hatj+4hatk`
`Now, oversetrightarrow(AB)xxoversetrightarrow(AB)=oversetrightarrow(A)=(3hati-2hatj+4hatk)xx(2hati+5hatk)`
`=i(-10-0)+hatj(8-15)+hatk(0+4)=-10hati-7hatj+4hatk`