If `veca' = hati + hatj, vecb'= hati - hatj + 2hatk` and `vecc' = 2hati - hatj - hatk` then the altitude of the parallelepiped formed by the vectors, `veca, vecb and vecc` having base formed by `vecb and vecc` is ( where `veca'` is recipocal vector `veca) ` `(a)1` `(b)3sqrt2//2` `(c)1//sqrt6` `(d)1//sqrt2`

Options

A. 1
B. `3sqrt2//2`
C. `1//sqrt6`
D. `1//sqrt2`

Answer

d

Explanation

Volume of the parallelpiped fomed by, `veca'vecb', and vecc', ` is 4.
therefore , the volume of the parallelpiped formed, by `veca.vecb and vecc is 1/4`
` vecb xx vecc = [veca vecb vecc] vec' = 1/4 veca'`
` |vecb xx vecc| = sqrt2/4 = 1/(2sqrt2)`
Length of altitude `1/4 xx 2sqrt2 = 1/sqrt2`