If → a = ˆ I − 2 J + 3 → K , → B = 2 ˆ I + 3 ˆ J − 5 ˆ K , Prove that → a and → a × → B Are Perpendicular. - Mathematics

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Sum

(a)  If `veca  =  hati - 2j + 3veck , vecb = 2hati + 3hatj - 5hatk,` prove that `veca and vecaxxvecb`  are perpendicular.

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Solution

`bara = hati - 2j + 3k` 

`barb = 2hati + 3hatj - 5hatk`

`baraxxbarb=|(hati   hatj   hatk ),(1 -2   3 ),(2    3  -5)|`

                   `=hati (10 - 9 ) - hatj (-5 -6)+hatk (3+4)`

                    `= hati + 11hati + 7hatk`

`bara.(baraxxbarb)=(hati - 2hatj + 3hatk). (hati + 11hatj + 7hatk)`
                             = 1 - 22 + 21 
                             = - 21 + 21
                             =0

`bara  ⊥ ^r bara xx barb`
`bara` is perpendicular to `bara xx b `

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2018-2019 (March) Set 1

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