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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 ____________.

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` | vecA _ 1 + vecA _ 2 | ^ 2 = | vec A _ 1 | ^ 2 + |vecA _ 2 | ^ 2 + 2 | vecA _ 1 | | vecA _ 2 | cos theta `
` 25 = 9 + 25 + 2 xx 15 cos theta `
` rArr cos theta = ( -3 ) / (10 ) `
` rArr vecA _ 1 . vecA _ 2 = | vecA _1 || vecA _ 2 | cos theta = 3 xx 5 xx ( ( -3 ) /(10)) = ( -9 ) /(2 ) `
` ( 2 vecA _ 1 + 3 vecA _ 2 ) . ( 3 vecA _ 1 - 2 vecA _ 2 ) = 6 | vecA _ 1 | ^ 2 - 3 | vecA _ 2 | ^ 2 + 5 vecA _ 1 . vecA _ 2 `
`= 54 - 150 + 5 (( - 9 ) /(2)) = - 118.5 `
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