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if (vecaxxvecb)^(2)+ (veca.vecb)^(2) = 1...

if `(vecaxxvecb)^(2)+ (veca.vecb)^(2) = 144 and |veca|=4` the find the value of `|vecb|`

Text Solution

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Since `(veca xx vecb)^(2) + (veca. Vecb)^(2) = 144` if the angle between `veca and vecb is theta`. Then
`|veca|^(2)|vecb|^(2) sin ^(2)theta + |veca|^(2).|vecb|^(2)cos^(2)theta=144`
`or |veca|^(2)|vecb|^(2) = 144`
`or |veca||vecb|= 12`
`or 4 |vecb|=12`
`or |vecb|= 3`
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