Question

The sides of a parallelogram are `2 hati + 4 hatj -5 hatk and hati + 2 hatj + 3 hatk `, then the unit vector parallel to one of the diagonals is
A. `(1)/(7) (3 hati + 6 hatj - 2 hatk ) `
B. `(1)/(7) (3 hati - 6 hatK - 2 hatk ) `
C. `(1)/(7) (-3 hati + 6 hatj - 2 hatk ) `
D. `(1)/(7) (3 hati + 6 hatj + 2 hatk ) `

Answer 1

Correct Answer - A
Let
` vec a = 2 hati + 4 hatj - 5 hat k , vec b = hati - 2 hatj + 3 hat k .`
The diagonals of the parallelogram are
`vec p = vec a + vec b , vec q = vec b -vec a `
`rArr vecp =3 hati + 6 hatj - 2 hat k , vecq= - hati - 2 hatj + 8 hatk `
So, unit vectors along the diagonals are
`(1)/(7) (3 hati + 6 hat j - 2 hatk ) and (1)/ (sqrt(69)) (-hati - 2 hatj + 8 hatk ) `
Hence, option (a) is correct.