If ` vec a^'= hat i+ hat j , vec b^' hat i- hat j+2 hat ka n d vec c^'2 hat i+ hat j- hat k ,` then the altitude of the parallelepiped formed by the vectors ` vec a , vec ba n d vec c` having base formed by ` vec ba n d vec c` is (where ` vec a '` is reciprocal vector ` vec a ,e t cdot` ) `1` b. `3sqrt(2)//2` c. `1//sqrt(6)` d. `1//sqrt(2)`

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`