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प्रश्न
Given `overset->a = 2hati - hatj + hatk, overset->b = 3hati - hatk and overset->c = 2hati + hatj - 2hatk`.
Find a vector `overset->d` which is perpendicular to both `overset->a and overset->b and overset->c · overset->d = 3`.
उत्तर
`overset->a = 2hati - hatj + hatk`
`overset->b = 3hati - hatk`
`overset->c = 2hati + hatj - 2hatk`
`overset->d = (xhati + yhatj + zhatk)`
since, `overset->d` is perpendicular to `overset->a and overset->b`
`overset->d · overset->a = (xhati + yhatj + 2hatk)( 2hati - hatj + hatk)`
= 2x − y + 2
`overset->d · overset->b = (xhati + y hatj + zhatk)(3hati - hatk)`
= 3x − z
`overset->c · overset->d = (2hati + hatj - 2hatk)(xhati + yhatj + zhatk)`
= 2x + y − 2z = 3
On solving x = 3, y = 15, z = 9
vector d = `xhati + yhatj + zhatk`
= `3hati + 15 hatj + 9hatk`
