The area of the triangle formed by the adjacent sides with `vecA = 3hati + 2hatj - 4 hatk and vecB = -hati + 2hatj + hatk` is

Options

A. `(sqrt(165))/(2)` units
B. `(sqrt(137))/(2)` units
C. `sqrt(165)` units
D. `sqrt(137)` units

Answer

A

Explanation

`vec(A)xxvec(B)=|{:(hati,hatj,hatk),(-3,2,-4),(-1,2,1):}|`
`=hati[2+8]+hatj[4+3]+hatk[-6+2]`
`=10hati+7hatj-4hatk`
`:.|vec(A)xxvec(B)|=sqrt(10^(2)+7^(2)+4^(2))=sqrt(100+49+16)=sqrt(165)`
Area of triangle `=(1)/(2)|vec(A)xxvec(B)|=(sqrt(165))/(2)` units