Let | vec A 1 | = 3 , | vec A 2...

Let ` | vec A _ 1 | = 3 , | vec A _ 2 | = 5 and | vecA _ 1 + vecA _ 2 | = 5`. The value of ` ( 2 vec A _ 1 + 3 vecA _ 2 ). (3 vecA _ 1 - 2 vecA _ 2 ) ` is ____________.

`-99.5`

`-118.5`

`-112.5`

`-106.5`

Text Solution

Verified by Experts

The correct Answer is:

`(vec(A)_(1)+ vec(A)_(2)).(vec(A)_(1) + vec(A)_(2))= |vec(A)_(1)+ vec(A)_(2)|^(2)`
`9+25+2 (vec(A)_1).vec(A)_(2))= 25`
`(vec(A)_(1).vec(A)_(2))= (-9)/(2)`
`rArr (2 vec(A)_(1) + 3vec(A)_(2)). (3vec(A)_(1)-2vec(A)_(2))`
`=6 |vec(A)_(1)|^(2)- 4 vec(A)_(1). vec(A)_(2)+ 9vec(A)_(2)- vec(A)_(1)- 6 |vec(A)_(2)|^(2)`
`=6A_(1)^(2)- 4A_(1).A_(2) + 9A_(1).A_(2)- 6A_(2)^(2)`
`=6 xx 9 +5 xx ((-9)/(2))- 6 xx 25 = -118.5`

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