Find the scalar and vector products of two vectors. `a = (3hati – 4hatj + 5hatk) and b = (– 2hati + hatj – 3hatk )`

Explanation

Scalar product
`veca.vecb=(3hati-4hatj+5hatk).(-2hati+hatj-3hatk)`
`=-6-4-15`
`=-25`
Vector product
`vecaxxvecb=(3hati-4hatj+5hatk)xx(-2hati+hatj-3hatk)`
`=|(hati,hatj,hatk),(3,-4,5),(-2,1,-3)|`
`=hati[(-4)(-3)-(5)(1)]-hatj[3xx(-3)-(5)(-2)]`
`+hatk[(3)(1)-(-4)(-2)]`
`=hati[12-5]-hatj[-9+10]+hatk[3-8]`
`vecaxxvecb=7hati-hatj-5hatk`
If, `vecbxxveca`, then `-7hati+hatj+5hatk`