Consider three vectors `veca , vecb and vecc`
Statement 1: `vecaxxvecb = ((hatixxveca).vecb)hati+ ((hatj xx veca).vecb)hatj + (hatk xxveca).vecb)hatk`
Statement 2: `vecc= (hati.vecc)hati+ (hatj .vecc) hatj + (hatk. vecc)hatk`

Options

A. Both the statements are true and statement 2 is the correct explanation for statement 1.
B. Both statements are true but statement 2 is not the correct explanation for statement 1.
C. Statement 1 is true and Statement 2 is false
D. Statement 1 is false and Statement 2 is true.

Answer

a

Explanation

Statement 2 is true (see properties of dot product)
Also ` (hatixxveca) .vecb=hati. (veca xxvecb)`
`Rightarrow veca xxvecb = (hati. (vecaxxvecb))hati+ (hatj. (vecaxxvecb))hatj + (hatk. (veca xx vecb))hatk`